It was a bold approach by Klopp, and he was rewarded after just nine minutes, with Grujic creating Liverpool’s opener.
With the Reds on the break, the Serbian’s deflected shot fell into the path of Sturridge, who poked the ball past Michel Vorm to make it 1-0.
Alberto Moreno, making his first start for Liverpool since September 20, was lively throughout, enjoying a fierce duel with Spurs right-back Kieran Trippier.
Sturridge had further chances to put Liverpool ahead before the break, but he was unable to beat Vorm again despite showing a strong partnership with Divock Origi up front, with Jonathan Moss calling for half-time at 1-0.
Mauricio Pochettino’s side looked to put the Liverpool defence to the sword after the break, with Estonian centre-back Ragnar Klavan struggling to gain a foothold on the contest.
But, as is often the case with Klopp’s Reds, their attack was there to bail them out, with Sturridge finally slotting past Vorm for his second on the hour mark.
Origi and Georginio Wijnaldum were instrumental in threading Sturridge through one-on-one to make it 2-0, with the Dutch midfielder clearly delighted with his team-mate’s effort.
Klopp was able to introduce peripheral figure Danny Ings with 22 minutes to play, with the striker brought on to a great reception from Anfield.
But with Ings missing a promising opening shortly after, Spurs went up the other end and won a penalty, with Vincent Janssen beating Simon Mignolet from the spot after Lucas Leiva had fouled Erik Lamela.
The Reds were able to hold on, however, and Klopp charged onto the field at full-time to embrace his much-changed side.
Liverpool are now 10 games unbeaten in all competitions, for the first time in a year, and can now look towards the League Cup quarter-final draw on Wednesday night.