The Merseysiders made much of the running and probably deserved the three points in front of their biggest gate of the season.
Bristol City were rarely seen as an attacking force and home keeper Gavin Ward enjoyed an easy 90 minutes. Gareth Taylor wasted a good early chance for Tranmere when heading over from a Chris Shuker cross.
Then City keeper Adriano Basso produced a superb fingertip save to turn a Chris Greenacre header away for a corner.
Taylor mis-kicked in front of goal when he had a chance and Chris McCready fired over following a free-kick.
City finished the first half well and Jennison Myrie-Williams' angled effort was well held by Ward. Scott Murray saw a shot deflected for a corner and then Richard Keogh blazed over from the edge of the box.
Tranmere regained control after the break and Basso did well to hold onto a powerful header by Ian Goodison following a Kevin Ellison free-kick.
Taylor headed just wide for Rovers on 65 minutes and Myrie-Williams headed wide for the visitors in a rare attack.
The only goal came after 85 minutes. Taylor headed down a Shane Sherriff cross into the path of Mullin who blasted home from 12 yards for his third goal of the season.
Goodison was immense for the winners and there were also lively contributions from Shuker, Ellison and Mullin.
David Noble worked hard in the City midfield but they were definitely second best on the night as they suffered a third defeat of the season on the road.