Rovers missed out on the chance to close the gap on the teams above them after going down 3-2 at home to Brentford.
In a pulsating advert for Championship football, poor defending proved costly as the Bees twice came from behind before winning the match six minutes from time.
Rovers started brightly with the returning Rudy Gestede blasting the home side in front after just five minutes.
But after former Rover Alan Judge had slammed a free-kick against the bar, Chris Long's deflected shot saw the visitors equalise just before the break.
There was still time for Rovers to go in at half-time with a lead, when Chris Taylor, who had twice gone close, fired in at the back post to make it 2-1.
However seven minutes into the second half the London club were level once more. Jota criminally given the freedom of Ewood Park to race forward unchallenged and he beat Jason Steele with a low shot.
Rhodes twice went close whilst Gestede blazed over, but it was the visitors who were the more clinical.
With just six minutes remaining a deflected Jota ball into the box saw Steele save well, but it rebounded off substitute Andre Gray and he walked it into the net to put them in front for the first time on the night.
Tom Cairney had the home side's best opportunity in the closing stages, but his curling effort went wide.
Hopes of a top six finish at the end of the season was always going to be an uphill task, but defeat to Brentford now leaves Rovers 11 points away with eight games to play.
Rovers made four changes from the side that defeated Charlton Athletic at the weekend and it was one of those returning who made an immediate impact at Ewood Park.
Just five minutes in a quick free-kick after Jordan Rhodes had been fouled on halfway sent Rudy Gestede powering to the edge of the box, and as defence and keeper stood off, the Rovers striker blasted home his 16th of the campaign in emphatic fashion.
It was a scintillating start from the home side and it should have been 2-0 on nine minutes. Ben Marshall getting around the back of the Brentford defence to cut back for Chris Taylor, but after getting the ball out from under his feet he slashed wide.
Despite the bright start from the home side the Bees were causing plenty of consternation at the back for Rovers.
On 16 a corner from Jota found Harlee Dean unmarked and his header seemed set to hit the back of the net only for a sensational save from Jason Steele.
A flowing Rovers move merited more after Tom Cairney centred, the ball coming out to Corry Evans who found Taylor but David Button in the visiting goal saved well low down.
Up until the half hour former Rover Alan Judge had had a quiet opening to the match, but after Alex Pritchard had been fouled by Alex Baptiste, the Irishman took the resulting free-kick and curled his shot against the crossbar.
Mark Warburton's side kept pressing and probing and a minute before the 45 they took full advantage of poor defending to equalise.
Chris Long was given far too much time and space on the right to race into the area and his shot deflected off Matt Kilgallon and into the back of the net.
But Rovers were to end the half in front, their hard work rewarded with a goal in added time.
A strong forward run by Evans saw him upended in the box, but as the referee waved play-on, Rhodes switched the ball to Taylor and he slammed it high into the roof of the net.
The start of the second half saw Marshall fire over a free-kick, whilst Cairney found the same set of fans with a shot from outside the box.
But those wasted opportunities would prove costly as the visitors struck in deadly fashion on 52 minutes.
Picking up possession after Marshall had lost the ball, play was quickly moved to the right to Jota and as Rovers parted, just as they had done in the first half, the Spaniard took full advantage to run unopposed to the edge of the box before beating Steele with a low shot into the corner.
In what was a terrific advert for Championship, Adam Henley then raced down the flank to deliver near post, Rhodes took the shot on first time, but it flashed narrowly off target.
Substitute Jay Spearing then clipped a ball over the top for Rhodes, but with time and space the striker opted to glance goalwards but the ball ran wide.
Strike partner Gestede would have a better chance following a flowing move involving Spearing and Spurr, but as the overlapping Taylor found the forward he could only blaze over.
It would be Gestede's last action as Chris Brown was sent on, reuniting the front pairing that had proved so successful in the last few outings.
Urged on by a vocal home support Rovers pushed forward, Taylor seeing a goal bound shot kept out by Harlee Dean.
But as they pressed, Rovers left inviting spaces at the back for Brentford to exploit which they would do six minutes from time.
Play was moved to the right to Jota who curled a shot goalwards that deflected horribly off Spurr, Steele saved superbly only to see the ball rebound off substitute Andre Gray and into the back of the net.
Rovers appealed for offside, but their appeals were in vain.
Tom Cairney, looking for his first goal since August, went the closest for Rovers in the final minutes, latching onto a Rhodes knockdown, the midfielder let fly but with Button scrambling across his box the ball bounced inches wide.
The Rovers pressed until the end, but their efforts fell short, to leave the prospect of a top six finish looking increasingly unlikely.
ROVERS: Steele, Henley, Baptiste, Kilgallon (c), Spurr, Taylor, Evans, Cairney, Marshall (sub Spearing 58 mins), Gestede (sub Brown 74 mins), Rhodes.
Subs not used: Eastwood (GK), Williamson, Songo'o, Lenihan, Mahoney.
Goals: Gestede 5 mins, Taylor 45+3 mins.
BRENTFORD: Button, Bidwell, Dean, Douglas (c), Odubajo, Dallas, Judge (sub Diagouraga 64 mins), Pritchard (sub Toral 77 mins), Jota, Tarkowski, Long (sub Gray 71 mins).
Subs not used: Bonham (GK), Craig, McCormack, Smith.
Goals: Long 44 mins, Jota 52 mins, Gray 84 mins.
Booked: Judge, Dean.
Attendance: 13,382 (including 457 visiting supporters)