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:
9. Luke Molyneux 7
Provided the free-kick which led to Olowu's goal. Nice connection being forged with him and Emmanuel down that right flank. Photo: Howard Roe/AHPIX LTD
10. Billy Sharp 6
Had to keep dropping short and going deep in his own half to get involved. That being said, had a few sniffs and caused Tranmere's defence another kind of problem - leading to Davies' red card. Photo: Howard Roe/AHPIX LTD
11. Jordan Gibson 7
Some really encouraging contributions, with some cute touches and clever through-balls from out wide on the left. Unlucky to not find the scoresheet. Photo: Howard Roe/AHPIX LTD
12. Joe Ironside 6
Caused a nuisance when he came on and hit the side-netting with the very last kick of the game. Photo: Howard Roe/AHPIX LTD