Rovers earned their first point of the season but it should have been all three at Ewood Park.
Owen Coyle's side seemed set to claim their first win in the first ever meeting with Burton Albion until Tom Naylor equalised two minutes from time.
Craig Conway opened the scoring for Rovers with a stunning strike on 26 minutes. The Scot cutting in from the right before slamming the ball home off the underside of the crossbar from 25-yards.
But Rovers couldn't build on their advantage and Burton levelled just before the break through Jackson Irvine.
Rovers regrouped in the second half and regained the lead just past the hour with Sam Gallagher marking his home debut with a fine headed goal.
But the home side again couldn't hold onto their lead with Naylor popping up at the back post to meet a corner from Matt Palmer to ensure the points would be shared.
Rovers made two changes from the side that faced Cardiff City on Wednesday night.
With Shane Duffy serving a one-match suspension it meant a debut in defence for 18-year-old Scott Wharton. Whilst Sam Gallagher, who impressed as a second half substitute at the Cardiff City Stadium, got the nod ahead of Anthony Stokes who dropped to the bench.
The visitors named an unchanged XI following their midweek win over Sheffield Wednesday, former Rover Lee Williamson named amongst the substitutes.
Rovers edged the opening exchanges at Ewood but without ever getting an effort on goal in the first 15. A Ben Marshall cross almost caught out Burton keeper Jon McLaughlin, before the wideman fed the ball through to Gallagher, but Kyle McFadzean got back in the nick of time.
Gallagher was showing some neat touches on his Ewood debut, and in the 19th minute he collected a forward pass from Stephen Hendrie to turn and shoot goalwards, but his effort flew over the bar.
Rovers finally got the breakthrough they had been threatening just past the midway point of the first half. There seemed little on as Danny Graham fed Craig Conway on the right. But the Scotsman drove inside before hitting a sumptuous 25-yard left-footed strike that flew in off the underside of the crossbar.
But instead of imposing themselves on Burton in the remaining minutes of the half, it was the visitors who took a grip of the game.
They'd given clear warning as to their attacking threat when Lloyd Dyer picked out Irvine on 36 minutes, but from close-range the midfielder couldn't keep his effort down.
He'd have no such trouble seven minutes later when he escaped his marker to meet a centre from Brewers captain John Mousinho to stoop to head home unmarked from 10-yards out.
With four minutes of injury time to play at the end of the half it was Rovers who were firmly on the back foot. Lucas Akins glanced over a header from a Matt Palmer corner kick, before Rovers were grateful that it was all square at the break as Jason Steele tipped over a shot on the run from Naylor.
Burton threatened at the start of the second half but it was Rovers who had the better chance to go in front on 50 minutes.
After a fine run from Gallagher was illegally halted by Mousinho, Conway took the resulting free-kick, but with his back to goal Hope Akpan couldn't keep his flicked header on target.
Former Rover Lee Williamson replaced Mousinho soon afterwards, but it was the Ewood club who were on the up. Conway firing narrowly over from the angle before Graham was denied with a near post shot.
But it was the Brewers' Tom Naylor who very nearly topped Conway's first half strike with an effort from a near-identical position, the midfielder's rasping drive coming back off the corner of post and bar.
However it was Rovers who went back on the attack and regained the lead just past the hour mark.
It came from a Conway corner, his ball in from the left perfectly met by the head of Gallagher as the striker powered the ball into the back of the net.
Rovers continued to see more of the ball, but neither side had meaningful opportunties until two minutes from time.
After winning a corner on the far side, Palmer sent the ball to the back post to where Naylor squeezed his header home.
Five additional minutes were shown at the end of the game, but there was no addition to the four goals that had been scored as the match ended all square.
ROVERS: Steele, Lowe (c), Greer, Wharton, Hendrie, Marshall (sub Feeney 84 mins), Akpan, Byrne (sub Lenihan 61 mins), Conway, Gallagher, Graham (sub Stokes 73 mins).
Subs not used: Raya (GK), Guthrie, Mahoney, Doyle.
Goals: Conway 26 mins, Gallagher 62 mins.
Booked: Graham 15 mins, Lowe 58 mins.
BURTON: McLaughlan, Mousinho (sub Williamson 51 mins), McFadzean, Turner, Palmer, Naylor, Akins, Irvine, Dyer, Beavon (sub Butcher 62 mins), O'Grady (sub Choudhury 86 mins).
Subs not used: Bywater (GK), McCrory, Fox, Delaney.
Goals: Irvine 43 mins, Naylor 88 mins.
Booked: Mousinho 49 mins.
Attendance: 10,356 (including 477 visiting supporters)