Steven Gerrard’s side were on top for most of the game and created several chances throughout the 90 minutes at Prenton Park but the hosts scored with one of their few chances of the game, midfielder Kieron Morris netting with a long-range effort ten minutes before the interval.
New signing John Lundstram made his first appearance in a Rangers shirt while there were also starting berths for Jack Simpson, Jermain Defoe, Glenn Middleton, and Scott Wright.
There were several absentees in light blue, owing to a mix of international duty and injury, but still plenty of first-teamers available for selection.
Ianis Hagi and Wright both had early efforts off target while Defoe scooped a chance just over the bar before Kemar Roofe just failed to connect with a James Tavernier cross.
Tranmere ‘keeper Joe Murphy then blocked an effort by Wright, with Defoe’s follow-up header blocked on the line and Roofe smashing the rebound into the stand behind the goal.
Following the stramash, Paul Glatzel tried to pick out Jay Spearing with a cross but the former Liverpool youngster was inches away from connecting with the ball.
From a corner, the home side took the lead; Morris hitting a sumptuous low drive from all of 25 yards that Allan McGregor had little chance of stopping.
The Gers sought a quick reply and Tavernier set up Defoe for another chance but the veteran striker knocked it just wide of the back post.
Gerrard made ten changes at the break, as he had done in Monday’s pre-season victory against Partick Thistle, and despite the alterations Rangers remained on top.
Youngsters Lewis Mayo and Stephen Kelly were introduced in defence and midfield while George Edmundson and Jordan Jones, who spent the second half of last season on loan at Derby and Sunderland respectively, were also introduced, along with Brandon Barker who scored three times in 19 games for Oxford United during a loan spell last term.
Winger Ryan Kent was first to go close for the Scottish champions, firing just wide from Calvin Bassey’s cross, before Murphy denied Cedric Itten who tried his luck from the edge of the box after good build-up play by Joe Aribo.
Bassey continued to cause problems for the League Two side and Joe Maguire had to be alert to clear another dangerous centre from the former Leicester City kid.
Jones then set up Itten again but the Swiss striker was crowded out and unable to direct his shot on target.
Kent then stepped up and saw a free-kick deflected behind for a corner before Aribo fed Lewis Mayo, whose effort was blocked by a number of Tranmere players on the goal-line.
Second-half substitutes combined for Rovers as Peter Clarke got his head to a Liam Feeney corner but couldn’t find the target.
Murphy then did well to hold another Kent effort from distance before pulling off a spectacular save to deny Aribo an equaliser in injury time.
Rangers’ next pre-season meeting is the visit of Arsenal on Saturday, July 17 with Mikel Arteta returning to Ibrox following a two-year spell in the early noughties.