Stephen Fletcher set Wolves on their way in the fifth minute with his sixth goal of the season, and although Rovers remained in the hunt up until the hour mark, they fell apart from that point.
In front of a sparse 10,031 Molineux crowd, those in attendance were at least warmed on a chilly night with further goals from Geoffrey Mujangi Bia, Kevin Doyle, Matt Jarvis and David Jones.
It could have been so very different if Doncaster had taken the one gilt-edged chance that came their way in the third minute.
In tinkering with his back four, as Wolves boss Mick McCarthy opted to do, there was scope for trouble.
In resting Stephen Ward and with George Elokobi suspended from the initial tie at the Keepmoat Stadium following his red card in that 2-2 draw, McCarthy was effectively without a recognised left-back.
It resulted in him switching Ronald Zubar from right-back to left and bringing in Stephen Mouyokolo to fill the vacancy, with both men playing in their new positions for the first time.
After 16 matches on the sidelines with a hip injury, Jody Craddock was restored to the centre of defence, leaving Christophe Berra on the bench.
So it was with a degree of consternation for a few fleeting moments that Wolves’ untried backline was tested so early in the game.
Dean Shiels, a late replacement for Martin Woods who suffered a groin strain in the warm-up, delivered a delightful low cross in behind the new-look Wolves rearguard for Billy Sharp to run onto.
With only Marcus Hahnemann to beat, the 11-goal forward could only rifle his drive against the advancing American.
The importance of such a save and Sharp’s effective miss became all too apparent just two minutes later as Wolves scored the only goal of the first half.
Doyle initially combined with Stephen Hunt down the left, with the latter then whipping in a piercing delivery for Fletcher to glance home from eight yards beyond Neil Sullivan.
The remainder of the half then belonged to Wolves who were far more the imposing side, save for one header from James Hayter in the 11th minute that was narrowly wide.
Instead, it was the Barclays Premier League side who should have headed into the break with a more comfortable advantage against their npower Championship opponents.
Zubar and Mujangi Bia, a 21-year-old Belgian-born midfielder making only his third start, initially went close with edge-of-the-area drives either side of Hayter’s effort.
Mujangi Bia followed that up with a right-foot curler from 25 yards that was inches beyond Sullivan’s left-hand post before missing a sitter 11 minutes from the interval.
Breaking from deep via a move sparked by Doyle, Mujangi Bia played an incisive one-two with Fletcher, but with the goal at his mercy from 12 yards he could only blaze his chance over the bar.
Recognising it was a golden opportunity for Wolves to carve out a 2-0 lead, Mujangi Bia was given a playful kick up the backside from Hunt as retribution.
Mercifully for Wolves it did not prove costly as Mujangi Bia gained his just reward for his industry by finishing off a 61st-minute move with a powerful 12-yard drive for his first goal for the club.
Doyle had been the supplier on that occasion with a low cross from the left, and five minutes later he again shaped as if to play the role of provider from a similar position after turning James Chambers inside out.
But instead, arguably catching Sullivan by surprise, the Republic of Ireland striker squeezed an acutely-angled shot in off the right post for what was also his sixth goal of the season.
The comfortable scoreline allowed McCarthy to make the first of his substitutions, with Hunt replaced by Jarvis in the 69th minute, and five minutes later the midfielder added further emphasis to the scoreline.
Centre-back Richard Stearman played Jarvis into space and he finished expertly with a sidefoot shot beyond Sullivan for his first goal since mid-October.
Wolves were not finished, though, and in the third minute of injury time Jones swept home a Jarvis corner from 16 yards to give the midlands club their biggest win since a 6-0 victory over Gillingham in March 2003.