Jan Vertonghen opened the scoring in the eighth minute from a corner kick before Joselu equalised moments later.
Alli then headed in from a delicious Serge Aurier cross in the 18th minute to make it 2-1.
The visitors held on for all three points and here we rate the performances of their players.
Hugo Lloris – His defenders let him down at times but the woodwork offered him a bit of help. Made a smart save low to his right in the second half. 6
Serge Aurier – Great delivery for Alli’s goal but always looked suspect at the back, leaving his side unmanned time and again. 5
Davinson Sanchez – Superb in the opposition’s box – getting the assist for the opener – but poor in his own. Left Joselu completely unmarked for the equaliser. 6
Jan Vertonghen – Stabbed his effort over the line – just – for the opener and was Spurs’ best defender. 8
Ben Davies – A threat going forward, set up Moussa Sissoko well on one occasion with a drilled cross. 6
Moussa Sissoko – Produced a good save from Martin Dubravka in the second half. Got forward well from midfield at times. 6
Eric Dier – A rather quiet display as he did little more than recycle possession. 5
Lucas Moura – Showed glimpses of his quick feet but vulnerable when closed down quickly and lost possession often. 5
Christian Eriksen – Was predictably among Spurs’ sharpest on the pitch. Good delivery from the corner for the opener and made five key passes. 7
Dele Alli – Not an outstanding display soon after a draining World Cup but took his chance well. Wasn’t quite as sharp to put away the second opportunity that came his way though. 7
Harry Kane – Looked well off the pace, lacking match sharpness. His touch let him down at crucial moments. The August drought continues. 4
Mousa Dembele – Replaced Moura in the 68th minute and helped Spurs get a better grip in midfield. 6
Son Heung-Min – Added more pace in the final third in the closing stages. N/A
Luke Amos – Didn’t have much time to make an impact. N/A
The Brazil international was, until Chelsea signed Kepa Arrizabalaga this week, the world’s most expensive goalkeeper following his £65million move from Roma.
His recruitment is seen as a key piece of business for Liverpool, strengthening an area which has been open to criticism for several years.
Alisson came to pre-season training later than the main group because of his involvement in the World Cup and has played just two friendlies against Napoli and Torino in the last six days.
However, Klopp has no worries about the 25-year-old making an instant impact.
“Just be a goalkeeper. Be yourself, in this case, because he is very calm and laid back – and that helps,” said the Reds boss ahead of Sunday’s visit of West Ham.
“It’s about making the right decisions in the right moments. It’s all good. He’s settled really quick, as if he’s been here longer than two weeks. That’s all fine.”
One player who has impressed in pre-season is Daniel Sturridge, who appears to have safeguarded his future at the club for the time being at least.
At the end of the previous campaign, Liverpool were prepared to listen to offers of £20m for the injury-prone striker but that situation has now changed.
“He’s still here, and he played a good pre-season. He could do a lot of the sessions, to be honest,” added Klopp.
“I can’t remember a bad game off him in pre-season, which is good. I said it 500 times already; when Daniel is fit, nobody doubts him. I do not.
“He’s here, he’s in a good shape, hopefully he can bring that into the season.”
While Liverpool were the summer’s biggest spenders with a £170m outlay West Ham spent £61m on five players, including the club-record signing of Felipe Anderson for £40m and the acquisition of free agent Jack Wilshere.
They also have a new manager in Manuel Pellegrini, the former Manchester City boss.
“One of the very, very successful managers on this planet. He knows how football goes, so he’s a really good tactician and coach. That changes a lot of things,” said Klopp of his counterpart.
“If you go through the West Ham team, it could be completely different.
“It could be Arnautovic in the ‘9’, Yarmolenko and Felipe Anderson wide or Chicharito striker with Arnautovic behind in the ’10’.
“Behind them, Wilshere and Noble or whoever, then a new full-back, Cresswell back. It’s just a good football team.
“They are ambitious, clearly. People expect that we win, and we expect the same, but we know that between now and then there are 95 brutal minutes, and we have to be ready for that.
“It’s easy not to underestimate West Ham. Analysis is pretty non-existent at this stage, but no problem. I’m still looking forward to it.”
Paul Pogba pledged to continue giving his best for fans, team-mates and “the people that trust me” in the wake of renewed speculation about his Manchester United future.
Two years after returning to Old Trafford from Juventus in a world-record deal, the 25-year-old is reported to be so unhappy that he has informed executive vice-chairman Ed Woodward of his desire to leave.
United have denied that happened and the same outlet said that Mino Raiola, the player’s agent, had even struck a deal with Barcelona – the kind of interest that the club have vowed to reject.
A tense relationship with Jose Mourinho appears to be at the heart of it. Questions about their relationship were raised last term and the midfielder is said to have been annoyed by his manager’s comments around the World Cup.
Pogba only returned to training at the start of the week after helping France to win the tournament but he was thrust into the starting line-up on Friday and given the captain’s armband, when his penalty set United on course for a 2-1 win against Leicester.
“Of course it makes me proud, it makes me happy to wear this (armband) at a big club like Manchester United,” he said.
“Like I always say, I always give my best for the fans, for my team-mates, for the people that trust me.”
Put to Pogba that it looked like he was fully committed to United after a lot of things had been said about his position at the club over recent days, he added: “Well, like I said, I always give my best for the fans, for the team-mates and for the people that trust me.”
Pogba’s focus on trust seemed pointed, as did his post on Twitter shortly after the match.
“I’ll always give my best to the fans and my teammates no matter what’s going on,” he wrote, along with #pogfeelings.
All does not appear well behind the scenes, despite Mourinho saying on the eve of the Leicester match that when the media “repeat 1,000 times that my relationship with my players is not good, it’s a lie that (is) repeated 1,000 times”.
But it is not just the manager’s relationship with United’s players that has come under inspection, considering he was irked by executive vice-chairman Ed Woodward failing to strengthen the squad before the transfer deadline.
Mourinho said “football is changing, and managers should be called head coaches” after beating Leicester, who he flagged as a side that should not be underestimated as they “invest more than us”.
The comments from the Portuguese and Pogba are sure to see contentment behind the scenes come under bigger focus, but Friday’s win was a welcome boost at a time of apparent discontent.
“It’s three points, it’s what we wanted,” Pogba said. “Very happy.
“Of course the performance wasn’t the best, but it’s better to start like this and finish well than start very well and finish bad.
“We know the players, and myself as well, didn’t have a lot of training and we played a game.
“We knew we were not going to be fit, 100 per cent, but the most important (thing) was to start well the Premier League.”
Pogba’s early penalty was followed by Luke Shaw – a player who had endured a testy relationship with Mourinho – scoring his first goal for the club, meaning Jamie Vardy’s stoppage-time effort was little more than a consolation.
It was a decent start to the season considering the number of injury and fitness worries that United had to contend with, but Friday’s skipper is not getting carried away.
“So, it’s pretty early to speak about this now,” Pogba said when asked of their chances of success this term.
“We started with Andreas Pereira and Fred, and they played very well today.
“With the players that we have…of course we’re Manchester United, we have to look at the top of the league. That’s obvious.
“I mean, Manchester United, we have to show on the pitch, we have to play well, we have to be focused and we need people to trust us.”