A first-half header by Reuben Reid on 29 minutes was enough to ensure that Plymouth Argyle travelled back to Devon with all three points from Prenton Park.
Rovers manager Rob Edwards made two changes to the starting lineup which began Tuesday night's Johnstone's Paints Trophy win against Carlisle United. George Donnelly and new loan signing George Barker came into the side in place of Eliot Richards and Abdulai Baggie who were named as substitutes. Goalkeeper Peter Brezovan remained in the side with Owain fon Williams away on international duty with Wales.
Tranmere the first chance of the game on 4 minutes. Janoi Donacien did well to win the ball on the right flank and his low pass into the penalty area eventually found Kayode Odejayi who fired a left footed shot wide.
On 7 minutes, Plymouth had their first effort on goal. Bobby Reid picked up the ball 25 yards from goal and fired a low shot which Peter Brezovan was equal to in the Tranmere goal.
George Donnelly had a opportunity on goal with 20 minutes played. Odejayi held the ball up just inside the Plymouth half and spread play to the right where Donnelly cut inside and hit a powerful left-footed shot which Luke McCormick collected at the second attempt.
Argyle's Lewis Alessandra had a double strike at goal from 20 yards midway through the first half. His first attempt was blocked by Donacien with the ball bouncing back to the Plymouth number seven who volleyed his second effort over the crossbar.
Plymouth took the lead on 29 minutes after a sustained spell of possession. Anthony O'Connor swung in a cross from the right and the ball was headed home by Reuben Reid six yards out.
George Barker had his first chance in a Tranmere shirt after 33 minutes. Matt Gill found him 30 yards from goal and the forward, on loan from Swindon Town, turned and hit a powerful shot over the crossbar.
On 42 minutes, a corner from Jason Koumas from the right found Odejayi's whose effort hit a defender to take the sting off it and McCormick made a comfortable save as the sides went in at the break with the visitors one goal to the good.
Eight minutes after the break, Bobby Reid twisted and turned and hit a shot from 25 yards which went over the crossbar.
On 58 minutes, a quick counter attack saw Max Power played through down the right and his cross found the head of George Donnelly but McCormick made the save.
Donacien was putting in some good crosses from the right and he did just that on 65 minutes, finding Barker eight yards out but his header was saved by McCormick.
Five minutes later, a dangerous low cross by played in by Danny Holmes from the left but the ball evaded a decisive touch as it flew across the face of the goal and out for a Plymouth goal kick.
On 74 minutes, Brezovan made a double save, first to deny Plymouth substitute Deane Smalley and then he quickly got up to block an effort by Reuben Reid with his legs.
Tranmere made a treble substitution with 15 minutes remaining. Into the fray came Eliot Richards, Abdulai Baggie and Marc Laird in place of George Donnelly, Matt Gill and Max Power.
Baggie linked up well with fellow substitute Richards on 84 minutes with the Sierra Leone international hitting a left footed shot across the goal which McCormick parried before the ball was cleared by the Plymouth rearguard.
A minute later, Donacien cross from the right found Richards who flicked it across goal but agonisingly narrowly past the far post. But the pressure did not pay off as Plymouth held on to take all three points.
Tranmere: Brezovan, Donacien, Ihiekwe, Holness, Holmes, Gill (Baggie 75), Power (Laird 75), Koumas, Donnelly (Richards 75), Barker, Odejayi. Substitutes: Ramsbottom, Davies, Rowe, Kirby.
Plymouth: McCormick, Mellor, Cox, Nelson, Alessandra (Smalley 73), Reuben Reid (Morgan 86), Blizzard (Norburn 89), McHugh, O'Connor, Bobby Reid, Hartley. Substitutes: Bentley, Banton, Harvey, Bittner.
Referee: David Coote
Yellow cards: Hartley (77), Odejayi (77), O'Connor (88)