The Reds’ striker was an unused substitute in Saturday’s win over West Brom but needed less than 10 minutes to turn in instinctively from six yards.
Jurgen Klopp made 11 changes from the weekend, one more than Mauricio Pochettino, and it was Liverpool who created more in a scrappy affair.
The impressive Divock Origi laid on two clear chances that Sturridge wasted, but the pair combined again for the England striker to be sent clear and slide his second under Michel Vorm’s body.
Spurs – who started with eight players aged 23 or under – were by no means overawed but struggled in attack until Vincent Janssen slammed home a penalty when substitute Erik Lamela was fouled.
Sturridge curled against the bar with the outside of his left foot late on and substitute Danny Ings saw a one-on-one chance saved as Liverpool moved into Wednesday’s draw.