The England striker has now scored eight times in six Reds appearances in the competition, netting in each half to remind a seemingly sceptical Jurgen Klopp of his prowess.
Sturridge was one of the most senior players on show amid much rotation and his goals were enough to settle matters on Merseyside, despite Vincent Janssen's 76th-minute penalty bringing late tension and a flattering 2-1 scoreline.
Both sides have finished runner-up in the competition in the past two seasons but a glance at the teamsheet told a story about its current place in their priorities.
Of the 22 players that started for the clubs on Saturday only Eric Dier, captaining Spurs, was on duty again.
Liverpool handed a debut to 18-year-old local boy Trent Alexander-Arnold, with Ovie Ejaria and Kevin Stewart also involved, while the visitors gave a first start to Georges-Kevin Nkoudou in a young starting XI.
Nkoudou's evening began poorly, his slip handing Liverpool the opener as they swarmed on the error.
The waiting Marko Grujic sent a deflected shot into the box and Sturridge was quicker to react than Michel Vorm, stabbing home from close range.
Little more than a minute had passed when Sturridge went close again, collecting Alexander-Arnold's ball and curling a shot towards the top corner where Vorm palmed clear.
Tottenham were struggling to assert themselves and should have conceded again when Divock Origi's persistence resulted in a gilt-edge chance for Sturridge, who scuffed his shot from 12 yards.
The best hope for an equaliser was an Alberto Moreno mistake, of which there were a couple, or a set-piece, which are becoming a recurring issue for Klopp's squad.
The recalled Simon Mignolet was called on to make one save, blocking from Janssen at his near post but Liverpool seemed likelier scorers and came close when Grujic flashed wide to end a smooth attacking move.
For Spurs there had been flashes from Tom Carroll and moments of muscularity at the back from Cameron Carter-Vickers but little else of substance.
The search for Liverpool's second continued at pace after the restart.
First Origi, freed by Lucas' smart pass, centred for Sturridge who had the goal at his mercy but botched his connection.
Origi himself then had a rasping drive parried over and in the 64th minute Spurs buckled.
Georginio Wijnaldum took advantage of Spurs' high defensive line with a one-touch pass that sent Sturridge clear on goal
A finish did not desert him on this occasion and he slotted carefully past Vorm.
Both managers raided their bench after the goal, Victor Wanyama and Erik Lamela bolstering Tottenham while Klopp sent for Nathaniel Clyne and the seldom seen Danny Ings.
The Reds continued to dominate though, Ejaria growing in stature and Wijnaldum drawing a fine save with a free-kick.
But it was Tottenham who scored next, Lamela winning a soft penalty from Lucas
Janssen pumped it down the middle and suddenly the tone shifted.
Lamela had another reasonable penalty appeal when he tangled with Moreno but this time Jon Moss waved play on.
Sturridge struck the crossbar via a deflection and Ings worked Vorm with a powerful hit but Tottenham might just as easily equalised, with some nervy moments in the home defence.
Wanyama made Mignolet work late but four minutes of added time came to nothing.