A freak own goal and a thumping header from leading scorer Rob Hulse kept Crewe in fifth place in the Second Divsion table.
Danio Gradi's side struggled to make an impact in the visitors' box in the first half, as this local derby failed to crackle into any sort of life.
The main talking point was the bizarre manner in which Rovers' forward Jason Price was injured in the fifth minute, as he tried to charge down home keeper Clayton Ince's clearance.
Price took the full force of the ball in the midriff and collapsed in the six-yard box before being stretchered off with a suspected broken arm.
It hardly affected the Wirral side at that stage of the game and they came closest to breaking the deadlock. Simon Haworth robbed Hulse inside his own box and chipped Ince, only to see the keeper make a last gasp save when he clawed the ball from underneath his bar.
From the resulting corner kick Haworth glanced a header towards the far corner only to see Ben Rix clear from the goal line.
The game was still stuck in a rut when on-loan midfielder Tom Curtis blundered as he tried to clear Dave Brammer's arcing cross from the right wing. Tranmere keeper Keith Welch was rooted to his goal line as the ball bulleted off Curtis' head and past him from 18 yards out.
Crewe sealed the points, which keep them among the early frontrunners, when Hulse ran onto Kenny Lunt's in swinging free-kick and planted a firm header down the middle of the goal, with too much power behind it for Welch to react.
The home side could have added to their lead towards the end, when Efe Sodje's header was palmed over the bar by substitute keeper Eric Nixon, who could do nothing when Crewe substitute Dean Ashton crashed a header onto the post