Rovers lead early thanks to Tommy Spurr's eighth minute opener, but the sending off of Grant Hanley in 31st minute gave the visitors an hour to defend their lead.
Even when Grant Holt levelled for the Latics on 69 minutes, it still seemed that Rovers would hold on for a point until Emmerson Boyce pounced in added time at the end of the game to break their hearts.
'We are gutted to not be at least coming away with a point," said the Rovers boss after the game.
"I thought we started tremendously well, we were totally the better team and we got the goal.
"Obviously the sending off affected the game but we then showed unbelievable spirit and character.
"To say that is our third game in a week, the energy levels of our lot, I can't praise them enough.
"The players were magnificent, cheered on by a fantastic support.
"We leave here with our heads held high, but gutted that we didn't get anything from the game. We've done ourselves proud in terms of how we've dealt with ten men.
"The lads truly showed great courage today and the fact that so many of our fans stayed behind at the end to applaud them off speaks volumes."