The hosts started brightly but saw a series of chances come and go. Owen Bailey had an early sighter parried away before Patrick Kelly suffered the same fate.
Jordan Gibson then saw a chance deflected over the bar before Billy Sharp followed suit. Many Rovers fans were starting to think it was deja vu after recent DN4 struggles but just before half-time the breakthrough was made. Joseph Olowu headed home after Jay McGrath's knock-down from a free-kick to ease some of the pressure that had built up.
Luke Molyneux then produced a superb diving header that came back off a post as the hosts came within a lick of paint of doubling the lead.
Ted Sharman-Lowe bailed Rovers out at the start of the second half with two important saves to keep Tranmere at bay. Those stops proved crucial when just a minute later Tranmere skipper Tom Davies was given a second yellow card for a foul on Sharp.
Gibson and Molyneux both missed golden chances to make it 2-0 but Kelly finally gave the hosts some breathing space when he pounced on a loose ball, ran through on goal and produced a tidy finish for his first league goal.
Substitute Kyle Hurst added gloss with a third shortly after his introduction. The visitors did restore a bit of pride late on when their sub Sol Solomon made the most of a McGrath error and reduced the arrears but the three points were never in doubt.
The win sees Grant McCann's side move up to second in the table, ahead of the day's later games.
Here's how we rated the Rovers players today:
5. Brandon Fleming 7
Brought back in from the cold and had the number of the Tranmere winger down his side. Got forward with some buccaneering runs but there was the odd pass that was over-cooked at times. Photo: Andrew Roe/AHPIX LTD
6. Owen Bailey 7
Much more like it from the stand-in captain. Energetic and more involved in the good stuff Rovers produced. Booked early doors second half. Photo: Howard Roe/AHPIX LTD
7. George Broadbent 7
Another who took a fair old while to get into his stride but once he did he was impressive. Plenty of tackles and blocks with the odd quality pass chucked in for good measure. Photo: Howard Roe/AHPIX LTD
8. Patrick Kelly 8
Superb. Took a while to get going but was zippy and sprightly once he did. Full of energy as he buzzed about and got his first league goal thanks to a finish a striker would be proud of. Photo: Andrew Roe/AHPIX LTD