Both sides made the expected sweeping changes for the fourth-round tie, which included a debut for 18-year-old Liverpool defender Trent Alexander-Arnold while midfielder Georges-Kevin Nkoudou and defender Cameron Carter-Vickers started for Spurs.
The Reds took an early lead through Sturridge on nine minutes when the England forward converted a cross from 20-year-old Serbian midfielder Marko Grujic.
Sturridge was on target against after 64 minutes when he latched onto a pass from Georginio Wijnaldum and beat Spurs stand-in keeper Michel Vorm.
Tottenham reduced the deficit with 14 minutes left when Vincent Janssen converted a penalty after a foul by Lucas on Erik Lamela.
Sturridge was denied a hat-trick by the crossbar as Jurgen Klopp’s men progressed to the last eight.
Fellow Premier League pacesetters Arsenal are also through after beating Reading 2-0 at the Emirates Stadium, with another young side selected by manager Arsene Wenger.
Alex Oxlade-Chamberlain put the Gunners ahead on 33 minutes, after a mistake from Royals keeper Ali Al Habsi.
The result was put beyond the Sky Bet Championship side when Oxlade-Chamberlain got another on 78 minutes, via a deflection.
Hull made it into the quarter-finals with a 2-1 win at Bristol City.
Harry Maguire headed the Premier League side in front from a corner just before half-time.
It was 2-0 only two minutes into the second half when Michael Dawson nodded in from another Hull corner.
The Championship side netted a late consolation through a fine individual effort from substitute Lee Tomlin before Tammy Abraham saw an effort cleared off the line in the closing moments.
Championship leaders Newcastle romped to a 6-0 win over 10-man Preston at St James’ Park.
Aleksandar Mitrovic put the Magpies ahead on 19 minutes with a powerful header at the back post.
Preston were reduced to 10 men on 27 minutes when midfielder Alan Browne was shown a red card for an elbow on Newcastle midfielder Jack Colback, who had to go off with a head injury.
Mo Diame made it 2-0 on 38 minutes with his first goal since signing from Hull, with Matt Ritchie adding a third from the penalty spot on 53 minutes.
Mitrovic got his second of the night and a fourth for the home side just two minutes later, with Diame also netting a brace following a 25-yard drive with three minutes to go.
There was still time for subsitite Ayoze Perez to add a sixth as Rafael Benitez side coasted into the quarter-finals.
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