After a flurry of early chances, James Milner's 34th-minute penalty - after Sheyi Ojo was upended by Tranmere goalkeeper Scott Davies - handed Liverpool a deserved lead.
Marko Grujić then cut in on his right to bend a dipping strike into the bottom corner to double Liverpool's lead going into the break.
The Reds made 10 half-time changes but remained on top and Pedro Chirivella tapped in after Davies failed to contain Dominic Solanke's strike to make it 3-0.
Visitors field 22 players across the 90 minutes
As they did last year, Liverpool fielded two different XIs - a stronger line-up including Gini Wijnaldum, Milner, Roberto Firmino, Daniel Sturridge and captain Jordan Henderson - back for the first time since February 11 after a long-term foot problem - starting the first-half.
Without summer signing Mohamed Salah, who was forced to wait for his uncompetitive debut due to immigration protocol, Ojo was handed a chance to impress, while Trent Alexander-Arnold was picked over Nathaniel Clyne at right-back.
Micky Mellon's Tranmere fielded a strong starting line-up with new signing Ollie Norburn starting in midfield, fellow new boys Jack Dunn - who joined from Liverpool's Academy - and Elliot Rokka on the bench to start.
Both teams go close in a lively start
At the same venue that they opened their pre-season preparations last year, Liverpool could have been ahead on 44 seconds when Sturridge clipped a pass over the back-four to Ojo. But after taking it round Davies 15 yards out, the winger could only side-foot wide.
And inside just three minutes, Andy Cook had a chance to break the deadlock for Tranmere, heading wide from a left-sided cross in a fast-paced start.
The game's intensity belied its status as a curtain-raising friendly for both teams and Joël Matip somehow conspired to fire over the crossbar from a few yards after Lucas Leiva flicked on a header into his path at a corner.
Liverpool struggled to convert their dominance into clear-cut chances as the tempo settled and Sturridge's low drive from distance was well held by Davies.
Sturridge should have made more of a rebound minutes later, only to mis-control after Davies had parried Grujić's shot into his path in the six-yard box and allow Stephen McNulty to clear.
Liverpool failed to make more of their possession out wide, continually looking to Ojo down the left and Alexander-Arnold on the right, only for their final balls to be consistently repelled.
Milner penalty breaks the deadlock before Grujić adds a second
But the Reds' breakthrough finally came on 34 minutes when Ojo was brought down by Davies in the box and Milner fired into the bottom corner from the penalty spot.
Milner almost scored a second three minutes later, curling narrowly wide of the far post after cutting inside on to his stronger right foot at the edge of the box.
Liverpool's first-half XI then doubled their lead before half-time, Grujić - who enjoyed a prolific pre-season last year - bending a 25-yard strike into the bottom corner, too quick for Davies to get down to.
Tranmere threatened a response before the break as Cook's fine first touch and superior pace took him past Lucas but with 40 yards still to go to Karius' goal, Wijnaldum recovered to win the ball back.
Reds make it three after a raft of substitutes
Only Karius kept his place as Liverpool made 10 half-time changes as planned, Solanke coming on for his first outing since joining from Chelsea.
Joe Gomez was also handed a first senior run-out since January while Clyne, Ragnar Klavan, teenager Woodburn and returning duo Jon Flanagan and Lazar Marković - who both spent last season on loan at Burnley and Hull City - all came on.
Kent's burst of speed almost led to a third in the second-half's opening stages, his cross finding Marković who teed up Chirivella to try and stab an effort above Davies, though the 'keeper caught well.
But that third goal came on 50 minutes when Davies couldn't hold Solanke's strike on the turn and Chirivella tapped into an empty net as the Tranmere shot-stopper scrambled across his line to recover.
Woodburn penalty adds extra gloss
Liverpool's second-half eleven maintained their control of the game, Woodburn testing Davies, although their influence in the final third started to wane.
Karius was finally forced into his first meaningful action on 64 minutes when Gomez's undercooked header back to his 'keeper afforded Tranmere substitute Andy Mangan a shooting opportunity, but the German stood strong to block the attempt with his chest.
And with that, Karius was brought off with 18-year-old Academy goalkeeper Kamil Grabara handed his first ever involvement with the first-team in his place.
Any notable action was sparse until Kent's tricky solo run down the left, jinking past two defenders and slotting in Woodburn, who was fouled in the box. The 17-year-old stepped up himself to convert the visitors' second spot-kick of the evening and round off the scoring.
Liverpool had chances to put more past Tranmere, Marković wasting a good opportunity by blasting over the bar and Solanke firing straight at substitute goalkeeper Luke Pilling, but at 4-0, Jürgen Klopp's side ensured a dominant morale-boosting first win.