Sturridge showed his class throughout the game and an instinctive finish early on gave the hosts the lead. In truth, Sturridge could have had more than two on the night as he missed a number of chances.
The striker though did finally score his second goal midway through the second half to send Liverpool on their way to the next round.
Vincent Janssen got one back for the visitors from the penalty spot before the end but overall on the night the better team progressed to the next round.
Both managers made a host of changes for the game. Jurgen Klopp changed his entire starting eleven for the game while Mauricio Pochettino made ten changes to his team.
Sturridge gave the hosts the perfect start
From the start the game, both teams showed what their tactics were for the game as both sets of players were pressing each other high up the pitch.
The pressing worked perfectly for the hosts when a slip from Georges-Kevin N'Koudou gave the ball to Marko Grujic, who made his way into the box and his goalbound shot deflected the ball into the path of Sturridge, who stabbed the ball into the net past Michel Vorm to give Liverpool the perfect start.
Sturridge then almost made it two a couple of minutes later when a lovely curling effort from the striker was heading into the top corner of net but Vorm managed to get up well and touch the ball over the bar.
The hosts continued to push forward without having any decent chances to get a second goal.
Spurs fail to impress in the first half
The visitor's finally got into the game after the half-hour mark when a low driven shot from Janssen was well saved by Simon Mignolet, who had very little to do in the first half.
The pattern of the game continued in the second half as the hosts continued to have a number of chances.
Sturridge scored his second after a number of missed chances
Sturridge somehow failed to make it 2-0 when a cross from Divock Origi found the striker but instead of hitting the ball into the net, it hit him and went the to other way much to the disbelief of the home fans.
Origi then went extremely close a few minutes later when a thunderous strike from the striker outside the box saw Vorm at full stretch to keep the ball out of the net.
The hosts though did finally get their second goal when a free-flowing move saw Georginio Wijnaldum play Sturridge through one on one against Vorm and the striker confidently stroked the ball into the net to give the home side what they deserved.
Vorm really was the only reason that the visitors weren't further behind in the game as a well struck free kick from Wijnaldum was heading in the goal but a good save from Dutchman kept it out.
Janssen got one back from the penalty spot
It was an important save as out of nowhere Spurs got themselves back into the game when Lucas Leiva fouled Erik Lamela in the box and referee John Moss pointed to the spot.
Vincent Janssen stepped up to take it and sent Mignolet the wrong way to get his team back into a game that they didn't deserve.
Sturridge almost restored the hosts two-goal a few minutes later but he saw his deflected chip from outside the box come back off the bar with Vorm beaten in the goal.
Right until the end both teams pressed for more goals with Danny Ings seeing his shot well saved before the end by Vorm as the game ended with Klopp's side progressing to the quarter-finals.