Rovers are now seven games unbeaten in the Championship but will see a home stalemate with Wigan Athletic as a missed opportunity.
The chances were there for both sides, with Rovers coming closest to winning it in the second half when Danny Graham crashed a header against the upright.
Sam Morsy forced Christian Walton into a smart save late on but in truth the result was probably the fairest outcome in the chill at Ewood Park.
A frustrating night all round was added to when Bradley Dack was forced off with what looked like a serious knee injury midway through the second half.
The point moves Rovers closer to the play-off places, and we now sit just two points off the top six.
Tony Mowbray made seven changes to his starting team against the Latics, with the likes of Stewart Downing, Corry Evans, Dack and Graham all coming back in.
Dack returned following suspension but Tosin Adarabioyo missed out following a knock picked up in training earlier in the week.
Rovers started well enough, but struggled to test visiting goalkeeper Jamie Jones in the opening 20 minutes, but the same could be said for Wigan, with ex-Latics loanee Walton relatively untroubled until he was called upon to hold onto Michael Jacobs' shot from just inside the box.
Josh Windass was next to force Walton into a save, but his cross-shot was straight down the throat of his former team-mate midway through the half.
At the other end, Darragh Lenihan's downward header from a deep Stewart Downing cross had to be turned behind by Jones as both teams searched for the opener.
Chances were few and far between in what was a frustrating first half for Rovers, with both teams going into the break as they started the game.
Rovers were better after the break, but Jamal Lowe was closest to breaking the deadlock just after the hour mark when he unleashed an effort that flew a yard or two beyond Walton's right-hand post.
A break in play then saw Dack forced off with what looked to be a serious injury, with Lewis Holtby on to replace the talisman for the remainder of the game.
Graham cracked the crossbar when he connected brilliantly with Armstrong's delivery. His attempt beat Jones, but hit the upright before being hacked clear from danger.
The Latics came again and Walton had to beat away a curling effort from Morsy as the clocked ticked to the 80th minute.
From the resulting corner kick routine Walton had to be alert again, this time to flick away Cedric Kipre's header as the visitors grew in confidence.
That gave Rovers a kick up the backside and Rothwell forced Jones into a smart save before Lenihan's header was hacked off the line and Downing's right-footed scorcher deflected just wide.
Time was running out for a winner, and Rovers were thankful for Williams for getting in the way of Morsy's strike in the final minute of added time before Lowe flashed a header just wide.
A superb stop from Jones denied Holtby a moment later with an impressive save down low to his left after the German's effort flew through the bodies and looked destined to nestle in.
Despite a flurry of opportunities late on, neither team could find what would have been a dramatic late winner.
Rovers: Walton, Nyambe, Lenihan (c), Williams, Downing, Travis, Evans (Johnson, 60), Armstrong (Gallagher, 80), Dack (Holtby, 69), Rothwell, Graham.
Unused substitutes: Leutwiler, Bell, Brereton, Bennett.
Booked: Rothwell, 90.
Wigan Athletic: Jones, Morsy (c), Byrne, Robinson, Kipre, Naismith, Massey (Williams, 62), Jacobs, Lowe, Evans, Windass.
Unused substitutes: Marshall, Dunkley, MacLeod, Roberts, Pilkington, Garner.
Booked: Morsy, 38, Windass, 88.
Referee: Gavin Ward.