Rafael Benitez's men were full value for their victory in a largely one-sided contest which was decided by a moment of Yossi Benayoun brilliance just before half-time.
Liverpool will doubtless face tougher tests as their warm-up programme moves into Switzerland over the next week, but Benitez could have asked for little more from his team's first outing of the campaign in front of a sell-out crowd on the Wirral.
To add to Rafa's delight, Daniel Agger made a successful return to first team duty after an injury plagued year while Daniel Pacheco offered a tantalising glimpse into the future with a fine display on his debut appearance.
Liverpool dominated the early exchanges against a Tranmere side who seemed intent to sit back and soak up the pressure.
Spanish youngster Daniel Pacheco ? making his first ever start for the Reds ? was bright and lively in the opening stages and came close to breaking the deadlock with a curling shot towards the far post which missed Danny Coyne's goal by inches.
Pacheco went even closer shortly after the half hour mark when he latched onto a brilliant forward pass from Daniel Agger and after taking one touch to control the ball, he fired in a shot which Coyne did well to turn away to safety.
The Tranmere number one was comfortably the busier of the two goalkeepers on show, although there would have been little he could have done about a fierce Jermaine Pennant shot had it been a couple of inches lower and not bounced to safety off the top of the bar.
The goal Liverpool richly deserved finally arrived just two minutes before the end of the opening period ? and it was well worth waiting for.
Israeli Yossi Benayoun found himself in space down the left and after cutting inside onto his favoured right foot, he superbly floated a shot over the outstretched arms of Coyne and into the back of the net.
Benitez made seven changes at the break, handing debuts to new signings Diego Cavalieri and Philipp Degen.
Liverpool continued to control the flow of the play with Coyne forced into a smart stop to deny Plessis while Agger sent a long range drive flying over the goal behind which the travelling Kopites were housed.
Skipper Steven Gerrard received a standing ovation from all sides of the ground when he was introduced to the action with twenty minutes left to play, but by this time Rovers were working their way back into the game and went close to levelling the scores when Chris Curran headed wide from close range.
That was as good as it got for the home side though, who were always second best against a Liverpool squad who will jet off to their training base at Interlaken tomorrow buoyed by their first victory of the season.