Ilkay Gundogan scored twice and there were also goals for Sergio Aguero and Bernardo Silva as the Premier League leaders produced yet another commanding display in what is proving a remarkable season.
The result means the second leg of the last-16 tie at the Etihad Stadium next month should be a formality for City.
Their boss Guardiola said: “It’s an amazing result for the last 16 of this competition.
“The Champions League is (about playing) 180 minutes but we are almost there. I’m not saying it’s done because in football anything can happen but it’s an amazing result.
“We could have been 2-0 down but then we were 0-2 up. We were clinical and I am delighted with the performance.
“We kept our level, we fought hard and created chances to score. They were four amazing goals. Overall I’m delighted.”
Guardiola also paid tribute to Gundogan, who might even have claimed a hat-trick had Tomas Vaclik not saved from him in the closing stages.
Guardiola said: “He’s a guy with special qualities. He’s amazing with a good sense of goal.
“When I see him play I realise how we missed him last season. He is a special player with a lot of personality. He doesn’t feel pressure, he’s a top player.”
The emphatic nature of the victory means Guardiola may be able to rest players in the second leg but he is not looking that far ahead yet.
First City face Wigan in the FA Cup and Arsenal in the EFL Cup final, with tricky league games against the Gunners and Chelsea also coming before the Basel return fixture.
Guardiola said: “That’s so important but we have to be focused and it’s after Chelsea. It’s so important to focus on them and take another step in the Premier League.
“Vinny (Kompany) is back, Fabian (Delph) is back – a lot of players have come back from long-term injuries. That’s good for everyone and (Gabriel) Jesus and (Benjamin) Mendy are coming back. We’ll have almost the whole squad for this period when we will need everyone involved.”
Basel coach Raphael Wicky admitted his side were outplayed by a ruthless City side.
Wicky said: “They were very clinical, scoring three goals in the first half. We started well, we created chances and managed to win balls but, as I said yesterday, we needed a perfect night. We needed to take the opportunities and be clinical.
“But we conceded goals too easily and after we went 3-0 down I think the game was decided.”
It might well be Valentine’s Day on Wednesday but for football fans love will be in the air when the Champions League last-16 round continues with two key ties.
Whether you’re a neutral or a fan of Paris-Saint Germain or Real Madrid, it will be hard to not keep tabs on the Spanish capital as Neymar and Co aim to inflict more misery on the two-time defending champions on their home turf at the Bernabeu.
Wednesday will be the fourth time in Champions League history that matches have been played on Valentine’s day. We look at some of the matches which made it a day to remember or saw fans’ hearts sunk:
2017: PSG 4-0 Barcelona, last-16, first-leg
The Spaniards came into the match by breezing through their group with five wins out of six but in Paris they simply fell apart in extraordinary fashion. Spectators inside Parc des Princes and indeed around the world could not believe their eyes at what was unfolding in the French capital as Lionel Messi, Luis Suarez and Neymar looked anonymous with Angel Di Maria’s brace, Julian Draxler and Edinson Cavani sealing a famous 4-0 win to shatter the hearts of Barcelona fans.
2012: Bayer Leverkusen 1-3 Barcelona, last-16, first-leg
It was night when Alexis Sanchez struck his first Champions League goals in what was a dominant display at the BayArena. The Catalans were simply in a league of their own, enjoying 72 per cent of possession as they ran out comfortable winners. Sanchez slotted home in the first half before Michael Kadlec equalised for the Bundesliga side. Sanchez doubled his tally with a tap-in with Lionel Messi completing the 3-1 victory with a fine volley.
2001: AC Milan 1-1 Paris St-Germain, second group stage
By no means a classic but the stalemate at least ensured both sets of fans went home with a share of the spoils. For PSG fans, it was their first point of the second group stage although it was a game they really should have won considering AC Milan went down to 10 men after just 42 minutes when Roque Junior was dismissed.
Leonardo had put the home side in front at the San Siro before Nicolas Anelka fired in the equaliser soon after. Andriy Shevchenko could have won it for Milan but PSG held on for a point.
It is quite remarkable that Zidane needs to do what no coach has done before and win the Champions League three times in a row, after doing what no coach has done before and winning it back-to-back last year. That’s just how badly Real Madrid’s season has gone.
Staring up at Barcelona in La Liga from 17 points behind, losing to little old Leganes over two legs in the Copa del Rey and qualifying from the Champions League group stages behind Tottenham. It’s not a good look for any big club, let alone arguably the biggest of them all.
They are a team in dire need of competition of a freshening up – but no-one was accusing Real of complacency in the transfer market this summer.
Zidane is the 6th manager in Real Madrid’s history to reach 90 wins with the club:— Real Madrid Stats (@RMadrid_Stats) February 11, 2018
 Miguel Munoz
 Del Bosque
 Jose Mourinho
 Leo Beenhakker
 Luis Molowny
 ZINEDINE ZIDANE pic.twitter.com/Ed5AZv3C3L
The narrative was that no matter what anyone else did, they had the best players in the world in virtually every position and some of the finest young talent around in Marco Asensio and Dani Ceballos.
Least of all whom were questioning Florentino Perez’s inactivity was Zidane himself. He has staunchly defended his players and, refreshingly, has not made any excuses for their downfall. Nor has he come up with any answers.
Consequently, for the best part of two months, Real have existed for this moment and this moment alone – the Champions League’s return. It’s a feeling that Emery knows all too well.
Many like to believe that the tea lady could guide PSG to the Ligue 1 title but it’s not that simple as Monaco, Marseille and Lyon are all fine sides that could compete in any top-flight league in Europe.
But Ligue 1 simply does not have the prestige to save Emery, a man who was brought to the French capital in the first place because he won three Europa League titles in a row with Sevilla and was a good bet to conquer the grandest stage of them all with an all-star team.
As delighted as he may have been to watch Neymar and Kylian Mbappe walk through the doors of the Parc Des Princes it has left him with no wriggle room to fail.
So the two coaches who have won five of the last eight European trophies between them must again head to the continent – not only in search of success, but succour.