Sturridge struck a mere seven minutes into his debut with a composed finish before being replaced by Luis Suarez — who put the tie at the One Call Stadium to bed within moments of his introduction.
With Stewart Downing having already worked home goalkeeper Alan Marriott from the left edge of the box, Sturridge opened his Reds account, coolly sliding the ball into the net after an incisive Jonjo Shelvey pass.
The same pair combined in the 14th minute — Sturridge dwelling too long on this occasion and allowing Marriott to make the save. Downing broke clear midway through the period but his drive was blocked smartly by Chris Clements as the visitors searched for a second.
Shelvey and Sturridge swapped roles in the 28th minute with a well-timed one-two releasing the former with space in front him. But Marriott saved a poke goalwards with Shelvey under increasing pressure from Exodus Geohaghon.
Matt Green lashed an effort at Brad Jones — who stopped to his right — after Suso lost possession, before Sturridge danced around several challenges into the area and attempted to tee up Shelvey. Cleared.
As the period drew to a close, Sturridge had another chance to double the lead — latching onto a Shelvey through-ball once again but seeing his angled drive from the right tipped around the post by Marriott.
The hosts threatened an equalizer immediately after the restart, with Anthony Howell forcing Jones to punch his near-post strike out for a corner. Jamie Carragher then made a crucial block from the same player, and Louis Briscoe tested Jones as the home side sensed a goal.
With 52 minutes played, Carragher kept the Reds’ sheet clean with a superb sliding intervention to deny Green, a Briscoe blast was tipped wide and a goalmouth scramble included the visitors clearing off the line twice.
Sturridge was withdrawn for Suarez, who looked to put an end to home hopes with a fortuitous finish after being played in by Downing shortly before the hour mark.
Green slammed home a goal for Mansfield with just over 10 minutes left on the clock, but the Reds will now continue their Wembley quest against Oldham at the end of January.
Liverpoolfc.com journalists’ man of the match: Daniel Sturridge.