Town came from behind for the third time this season to book a place in the third round of the Capital One Cup with James Alabi marking his debut with a goal.
Blues needed extra-time to progress though, Brett Pitman’s goal cancelling out Andy Williams’ first-half opener for Doncaster.
Town finished the 90 minutes on top but couldn’t find a way past Thorsten Stuckmann in the home goal until David McGoldrick headed Blues in front in the first-half of extra-time.
Alabi then stabbed in a third for Mick McCarthy’s side before the break to put Town in command and Ryan Fraser rattled in his second goal in successive games and his third of the season to put the result beyond question.
Blues made eight changes from the team that won at Preston at the weekend, with only Tommy Smith and strike duo, Pitman and McGoldrick retaining their places as Town reverted to a similar line-up that got past Stevenage in the first round.
Josh Yorwerth, who scored in the 2-1 win over Boro, went close to giving Town an early lead, his header scrambled clear, then the ball escaped Jay Tabb inside the box from Pitman’s cross seconds later.
Tommy Smith was in the right place as Curtis Main looked to get in, while at the other end McGoldrick twisted and turned his way into the home box before testing Stuckmann who got down well to save low to his left.
McGoldrick and Larsen Toure combined to set Pitman through on goal but the summer signing from Bournemouth was well off target from the edge of the box.
McGoldrick ripped a shot just wide as Blues continued to carry a threat but it was Rovers who broke the deadlock on 23 minutes, Williams heading in at the far post from Cedric Evina’s cross.
Pitman responded for Town with a run deep into Doncaster territory but his cross was cleared, Adam McDonnell failing to trouble Stuckmann with a left foot effort from 20 yards.
Dean Gerken was quickly off his line to smother the danger from Williams as Rovers began to pose problems for Blues’ young backline, ex-Town loanees Richard Chaplow and Richie Wellens prompting Paul Dickov’s side from the centre of the park.
Yorwerth did superbly to stop James Coppinger making it two just past the half hour after a flowing Rovers move opened up the Town rearguard, Wellens then miscuing from Aaron Taylor-Sinclair’s free-kick as Doncaster looked the more likely to find the net.
Pitman had a gilt edged chance to put Blues level six minutes before the break though, Kenlock’s long ball over the top sent the striker through but his lob bounced back off the bar and McGoldrick hit the sidenetting from the rebound.
Town were almost level two minutes into the second-half, Pitman denied by Stuckmann with an excellent save from close range.
Williams then tested Gerken from the edge of the box as Rovers broke, the former Swindon striker then winning a free-kick 20 yards out after he was judged to have been brought down by Smith, Main lashing the ball wide.
Wellens sent Gerken scurrying back towards his goal with a speculative 40 yarder, the Town ‘keeper then beating out Billy Whitehouse’s effort before Blues levelled just short of the hour, Pitman smashing the ball home after it broke into his path 10 yards out.
Toure and Kenlock combined to release Tabb in the left channel but his cross beat Pitman at the far post, Yorwerth then getting on the end of Tabb’s free-kick but unable to get any power with his header.
Wellens curled over as a third round place remained up for grabs, Blues making a first change on 69 minutes with Alabi on for Pitman.
The former Stoke striker, who penned a one year deal at Portman Road on Monday, made an instant impact, powering between two defenders but he couldn’t force the ball past Stuckmann with his first touch as a Town player.
McGoldrick curled a beauty inches wide, then went even closer when he got on the end of a free-kick before Blues made a second change with Luke Chambers on for Smith.
Stuckmann produced another excellent save to deny Toure a first goal for Blues three minutes from time, the ‘keeper then repeating the heroics to tip over the midfielder’s right foot curler.
Town finished the 90 minutes on top, McGoldrick causing another nervous moment for the home side with a strike across goal but Doncaster held on to take the game into extra-time.
Cramp victim McDonnell made way for Fraser midway through the first-half of extra-time, Wellens firing wide from distance before Town got that vital second goal, McGoldrick heading in from Toure’s cross on 102 minutes.
Blues all but clinched that place in the third round just before the break when Alabi guided the ball in from McGoldrick’s shot and Fraser made sure with a left foot finish seven minutes from the end.
The win stretches Town’s unbeaten start to the season to six games ahead of the table-topping clash against Brighton at Portman Road at the weekend.