Ten-man Rovers, hoping for a third successive league win for the first time since 2007, went ahead through Tommy Spurr at the DW Stadium only to lose the momentum when captain-for-the-day Grant Hanley was dismissed for catching Nick Powell's face after half an hour.
Returning substitute Grant Holt made a crucial contribution in the leveller, helping to bundle home, although the final touch came off Spurr for a likely own-goal.
And Latics, who had hosted their first-ever European game on Thursday and seen the town's rugby league team complete a Super League Grand Final and Challenge Cup final double on Saturday, would claim all three points with Boyce's late header.
After the 3-1 Europa League victory at home to Maribor, Wigan boss Owen Coyle suggested goalkeeper Scott Carson could soon force his way back into the England reckoning.
But, just eight minutes in, he made the type of error which his international career was associated with.
A long free-kick from Tom Cairney should have been dealt with by the 28-year-old yet, in trying to claim above Leon Best's head, he spilt the ball into Spurr's path and the full-back lashed home via a deflection.
The hosts strove for an instant response and James McArthur's drilled effort fizzed just past the post.
However, given Rovers were on top and Coyle's side were displaying all the hallmarks of a European hangover, the moment of madness from stand-in skipper Hanley was puzzling.
Powell chased after Hanley and, after laying the ball off, the Scotland international stuck his arm straight into the Manchester United loanee's face with referee Stuart Attwell well placed to instantly brandish the red card.
The tide soon turned in Wigan's favour and Jordi Gomez and Powell both tested Jake Kean in the Rovers goal before the stopper produced a mishap to rival Carson's earlier gaffe.
Under heavy pressure from Leon Barnett, Kean fumbled a deep corner backwards on to his post before gratefully catching the ball at the second attempt.
Attwell's Sunday afternoon got no easier in the second half as he failed to award a penalty when Ben Watson's arms blocked Jordan Rhodes' shot, much to the dismay of the large travelling contingent.
Coyle then introduced Holt, appearing for the first time since August due to injury, to give Latics the out-and-out striker they have dearly missed in recent weeks.
And he made up for lost time by playing a huge role in the 69th-minute equaliser.
Gomez's corner found Latics' number nine and his header ended in the net via considerable assistance from Spurr, who got the crucial last touch.
It was all Wigan now and Powell could have turned the game completely on its head had he not fluffed his line moments later.
Meanwhile, Kean's shakiness at set pieces continued as he dropped a routine catch only to survive once more as Powell's goal-bond flick struck his leg.
James McClean twice went close and Kean clawed away from under his crossbar while, at the other end, Josh King disturbed the roof of Carson's net.
Then, a mere three days after he had led them out on that historic European night, Boyce popped up to glance Watson's free-kick in off the post to snatch victory and sneak Wigan into the top half of the table on goal difference.
Latics are one point and three places behind Rovers, and have two games in hand.