Rovers needed a victory to ensure league survival but it never looked on the cards against an efficient Bristol City whose play-off hopes remain after a fifth successive win.
City dominated the opening 45 minutes. They went ahead on 17 minutes with a 17th goal of the season for Steve Brooker.
He was left with an easy tap in after his header was parried by home keeper Matt Murray.
Tranmere were out of luck when Steve Davies hit the bar with a free-kick and he saw another effort blocked by the defensive wall.
The visitors doubled their lead on 34 minutes with a looping header by Mark McCammon from a pin-point cross by Bradley Orr.
Jason McAteer was the Tranmere player to be red-carded for elbowing McCammon.
Tranmere huffed and puffed in the second half but Steve Jennings missed the target and Gareth Roberts had no better luck with two good efforts.
Then Delroy Facey when clean through saw his shot blocked by City keeper Adriano Basso.
Craig Woodman netted from the penalty spot for Bristol with an excellent effort into the top left-hand corner in the 89th minute.
Substitute Carl Tremarco conceded the spot-kick by tripping City substitute Cole Skuse.