Tranmere failed to register a shot on target all game, and the difference between the two sides was Bees centre back Michael Turner's 20-yard strike in the 69th minute that made it 1-0.
The defeat means Rovers stay on 75 points - 10 behind City - with both teams having four games left to play. A win for City against Swindon at the KC Stadium on Saturday will make automatic promotion certain, regardless of what Tranmere do against Blackpool. A draw will be good enough as long as Tranmere don't win, while a Blackpool win will end any chance of Tranmere catching City. If results don't go City's way this weekend, promotion will be secured next time they win or Tranmere lose.
Meanwhile, last night's result sees top of the table Luton clinch promotion already. They have 88 points, and the maximum Tranmere can now achieve is 87.
The title is still up for grabs though, with just three points separating Luton and City.
Last night's game at Griffin Park was also a big one for Brentford themselves. They move up to 4th with a game in hand of all of their rivals, putting them in a strong position to qualify for the play-offs.