Ola Aina's header proved the difference as Rovers bowed out of the Emirates FA Cup at the third round stage after a narrow defeat to Championship side Hull City at Ewood Park.
The Chelsea loanee nodded home just before the hour mark to separate the two sides in an evenly fought encounter.
Rovers put up a fight against Nigel Adkins' Tigers, with substitute Danny Graham coming closest but try as they might, the hosts couldn't find the equaliser to send the tie to a replay.
Tony Mowbray made five changes to the XI which started the last game against Rotherham on New Year's Day with David Raya, Paul Downing, Richie Smallwood, Bradley Dack and Graham all either not in the squad or on the bench.
Jayson Leutwiler once again started in the competition inbetween the sticks, whilst there were opportunities from the start for Willem Tomlinson, Joe Nuttall and Dominic Samuel.
Opponents Hull went with a strong lineup and included top scorer Jarrod Bowen in their starting XI and incidentally, both skippers for the game - Mulgrew and David Marshall - are team-mates for the Scottish national team.
It was a strong start from the hosts and inside the opening two minutes Craig Conway curled just over the bar after Samuel's pass found the Scot.
Ten minutes later and a deep cross sat up nicely for the advancing Paul Caddis who caught the ball sweetly but saw his half-volley crack the crossbar and bounce clear.
Hull struggled to get out of their half in the opening stages but Michael Hector did force Leutwiler into a smart stop with a headed effort mid-way through the half at a chilly Ewood.
Ryan Nyambe was on hand to block a Adama Diomande effort moments later after Fikayo Tomori's low cross from the right side as the visitors grew into the game.
Mowbray was forced into a change just before half time with Corry Evans coming off with what looked like a knock and Lewis Travis replaced the former Hull man, in a half that in all honesty wasn't full of chances.
After the break the game finally came to life through young defender Aina's header to open the scoring for the visitors just before the hour mark.
The defender got above his man to get on the end of Bowen's inswinging corner and planted it past Leutwiler and into the net.
Mowbray changed things up soon after with Graham and Dack entering the action on the hour, with the latter involved almost straight away as his cross fell to Conway who drove at goal but saw Marshall save his powerful attempt.
Fellow substitute Graham had a golden chance to equalise with 21 minutes remaining, but, after being put through by Conway, the striker could only drag his effort inches past the post.
The visitors still looked dangerous on the counter and Bowen dragged wide after wriggling clear of his man with ten minutes remaining.
A couple of moments later and goalscorer Aina was fortunate to not receive a second booking after hacking down Conway as Rovers continued to press for an equaliser.
Injury time saw Graham flick a wicked Mulgrew free kick goalwards but Marshall produced a strong reaction save to deny Rovers and send Hull into the hat for the round four draw on Monday evening.
Rovers are next in action in the massive clash with Shrewsbury Town at Ewood Park on Saturday 13th January and the lads will need your support, so purchase your ticket(s) for the game, by clicking here.
Rovers: Leutwiler, Nyambe, Williams, Mulgrew (c), Caddis, Tomlinson (Dack, 60), Evans (Travis, 44), Bennett, Conway, Nuttall (Graham, 60), Samuel.
Substitutes: Raya, Hart, Downing, Wharton.
Booked: Williams, 30, Tomlinson, 44
Hull City: Marshall (c), Hector, Toral, Diomande (Campbell, 75), Bowen, Henriksen, Clark, Evandro (Irvine, 60), Tomori, Aina, Stewart (Meyler, 80).
Substitutes: McGregor, Meyler, Dicko, Clackstone, Hamilton.
Goal: Aina, 58
Booked: Aina, 72
Attendance: 6,777 (858 away)