For the first time under Tony Mowbray, Rovers played out a goalless draw at Ewood Park, but the encounter wasn't short of chances for both sides.
Millwall's best opportunities came in the first half, with George Saville and Steve Morison hitting the woodwork, but Danny Graham had two great chances in the second half to win the game, with visiting stopper Jordan Archer denying him both times.
For a 0-0, it was certainly entertaining, and Rovers will feel a touch unfortunate not to have garnered all three points, particularly after a stellar second half showing.
Mowbray named one change to the lineup from last weekend's draw at Ipswich, with Derrick Williams and Dominic Samuel missing out through injury, which resulted in Amari'i Bell and Kasey Palmer coming into the XI, respectively.
Neil Harris named an unchanged side to the one which drew 2-2 with Middlesbrough last week, and included former Rover Ryan Tunnicliffe on the bench at Ewood Park.
It was the Londoners who started brighter, with Jed Wallace slamming a volley just wide after being teed up with skipper Morison just two minutes into the encounter.
The Lions went even closer soon after, with neat build up play eventually concluded with Saville's shot from range crashing against the post and on the follow up, Lee Gregory was adjudged offside.
David Raya was grateful to the other post midway through the half as Morison found room but saw his strike from inside the box hit the woodwork and roll across the six-yard box before the danger was cleared.
With two minutes to go until the break, Bradley Dack had Rovers' best opportunity of the half, but his low free kick was shoveled over and away by Archer.
The next opportunity wasn't far away and Dack was involved again as his cross into the box found Darragh Lenihan, whose looping header clipped the top of the bar before bouncing out of play.
Six minutes into the second half and Graham had a great chance to break the dealock, but after racing away from Shaun Hutchinson and then shaking off the defender, but saw Archer in his way as he looked to sneak the ball in at the near post.
Moments later and Graham was denied again in almost a carbon copy chance as he once sgain shook off Hutchinson but saw the impressive Archer out quickly to smother and the score remained goalless.
Rovers were dominant and neat play from Graham and Palmer led to Elliott Bennett lashing wide from range as the home side upped the ante.
Substitute Joe Rothwell almost made an instant impact on his competitive debut, but his 25-yard belter stung the palms of Archer who did well to turn his strike around his left-hand post.
The chances were falling Rovers' way and Mulgrew hit another free kick just over the bar a minute or two later.
In the end, despite edging the game, Rovers couldn't find that decisive breakthrough and had to make do with a point for their efforts.
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Rovers: Raya, Nyambe, Lenihan, Mulgrew (c), Bell, Evans, Smallwood (Armstrong, 66), Bennett (Travis, 79), Dack, Palmer (Rothwell, 64), Graham.
Unused substitues: Leutwiler, Nuttall, Downing, Conway.
Millwall: Archer, Meredith, Hutchinson, Cooper, Williams, J. Wallace (Ferguson, 89), Gregory, Romeo, Morison (c), O'Brien (Skalak, 70), Saville.
Unused substitutes: Amos, McLaughlin, Tunnicliffe, Elliott, M. Wallace.
Booked: Williams, 44.
Referee: Gavin Ward.
Attendance: 13,239 (851)