Wigan scrum-half Paul Deacon is brought down by Rovers' Ben Fisher
Willie Mason ran in his first Super League try - but he could not stop champions Wigan getting back on the winning road at Craven Park.
Michael Maguire's men had not won in three matches to slip to fifth.
But first-half tries from Joel Tomkins, Ryan Hoffman and Josh Charnley set them on their way, bolstered by Thomas Leuluai's early second half effort.
And, although Rovers replied with tries from Matt Cook, Mason and Ben Cockayne, George Carmont's late score sealed it.
Wigan, who dropped England winger Darrell Goulding, crucially had stand-off Paul Deacon back from a head injury that has kept him out for four games.
Prop Jeff Lima returned from suspension and back row forward Liam Farrell was recalled to the squad.
But it was the imminent announcement of Wigan coach Michael Maguire's departure, which came after the game, which dominated the evening.
All the mayhem surrounding Maguire's future had to take a back seat when Tomkins, again playing at centre, capitalised on a Murrell error inside his own 10-metre line to open the scoring.
Pat Richards failed to convert but Rovers found themselves 10-0 down after 21 minutes when Hoffman strolled his way through.
The home side replaced Mason with Cook, who quickly scored. But, just three minutes later, Charnley, a fans' favourite at Craven Park at the end of last season after scoring five tries in five games while on loan, scored in the right-hand corner, Richards slotting the goal.
Rovers started the second half strongly, the restored Mason scoring his first Super League try.
But, after Murrell missed the goal attempt, Wigan showed why they are champions with a try shortly afterwards.
Leuluai scored from close range from a typical run from dummy half, Richards' right boot making it 22-10.
Richards then thought he had scored himself in the left corner but Rovers full-back Ben Cockayne bundled the winger into touch before he could ground the ball.
And, moments later, Cockayne set up a grandstand finale when he grounded Green's kick close to the posts.
Murrell's kick left only a converted try between the two sides. But, when Mason was penalised for a grapple tackle on his compatriot Hoffman, Richards gratefully accepted the cushion of two extra points that meant Rovers needed to score twice.
And the outcome was finally decided when Carmont slid over three minutes from time.
On the final hooter, Cockayne and Jeff Lima, only just back from his third suspension of the season, were put on report by referee Thierry Alibert after a late incident.
Hull KR coach Justin Morgan:
"We made too many errors in good field position. We got ourselves back in the game through a try and then we'd made a mistake from a kick-off.
"We were always chasing our tail but I thought we continuously turned up but the errors cost us."
Wigan coach Michael Maguire:
"We have been able to build a great team in my time here and this team will definitely be taking things forward for Wigan.
"The players are a great bunch and I really enjoy coaching them.
"They have worked so hard to achieve where we are and we are going to try and achieve a lot more this year."
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