Wes Burns scored twice and Kieffer Moore once as the Blues came from a goal down, scored by Tom Eaves, to give Town a 3-1 half-time lead over bottom club Rotherham United at Portman Road.
Town made three changes from the team which won 2-1 at Swansea on Saturday with Burns, Jeremy Sarmiento and Lewis Travis coming into the XI.
Burns returned on the right for Omari Hutchinson with Sarmiento on the left for Nathan Broadhead.
Travis started alongside skipper Sam Morsy in the centre of midfield for the first time with Massimo Luongo joining Hutchinson and Sarmiento on the bench.
The Millers made four changes from the team which lost 1-0 at home to Watford on Saturday with Sam Clucas, Tom Eaves, Lee Peltier and Jordan Hugill coming into the team for Cameron Humphreys, Sam Nombe and Charlie Wyke, who dropped to the bench, and Sebastian Revan, who was left out of the 20-man squad.
The game was less than a minute and a half old when the visitors took the lead from their first attack.
Luke Woolfenden and Harry Clarke seemed to get in one another’s way after Sam Clucas had brought a loose ball inside the full-back and the former Hull City man threaded through to Eaves, who confidently stroked past the advancing Vaclav Hladky to his left.
Town’s 13th goal conceded in the first 15 minutes in the Championship this season, more than anyone else in the division, caused frustration among the home support but not too much panic given the Blues’ comeback credentials.
After one or two passes had gone astray to a few moans - and Rotherham skipper Sean Morrison had been booked for a foul on Sarmiento - the Blues began to get their game together and in the 10th minute they levelled.
Morsy picked up the ball on the edge of the area following a free-kick and drove into the box before sending over a cross, which was met by Burns arriving at the far post, the Welshman nodding his fourth goal of the season across the face and into the corner of the net from 12 yards out.
Having got Town back on terms - via the 12th goal the Millers had conceded in the first 15 minutes of a Championship game this season - Burns wasn’t far away from giving his side the lead a minute later, bringing the ball forward into the right of the box before hitting a low shot across the face but just wide.
However, Town fans didn’t have to wait too much longer to see their team go in front.
On 14, Burns was again sent away on the right, this time by Clarke, the Wales international outpacing veteran Rotherham right-back Lee Peltier before sending over a low cross for Moore to slam home against the club where he made his name on loan from Town back in 2017.
The on-loan AFC Bournemouth man has now scored four times in four starts and one sub appearance since rejoining the Blues, while Rotherham now match Town for goals conceded in the opening quarter of an hour.
As the game reached the 20-minute mark, Moore spent some time undergoing treatment on the pitch, having already been seen by the physio prior to his goal. The Wales international returned soon afterwards but not looking entirely comfortable.
Rotherham subsequently had a brief spell of pressure, which ended with Ollie Rathbone hitting low shot through to Hladky.
But that didn’t last long and in the 29th minute, the Blues increased their lead. Burns was again sent away around the outside of Peltier and smashed a shot which Millers keeper Viktor Johansson saved with his right leg.
The ball bounced out to Leif Davis on the left of the area, the full-back rather mishit his strike but Johansson was only able to palm it out to Burns, who tapped home from the edge of the six-yard box.
Not long after the goal, the game was held up for a lengthy spell after Rathbone collided with the advertising hoarding after a challenge with Sarmiento, appearing to have hit his head. The midfielder was eventually taken down the tunnel on the stretcher cart and replaced by Femi Seriki.
As the half moved into its final five minutes, Burns almost completed his hat-trick. Sarmiento crossed deep from the left and the Welshman headed into the ground but just wide of Johansson’s left post.
Three minutes later, Chaplin left the ball for Moore on the edge of the area and the striker looked to have a sight of goal before turning into a defender, perhaps not having expected it to have been allowed to run to him by his teammate.
The fourth official’s board indicated an additional 10 minutes, which had been anticipated after the lengthy hiatus due to Rathbone’s injury and the earlier stops due to Moore’s knock.
Having established their two-goal lead, the Blues had one or two shaky moments during time added on, Hladky fumbling a ball when diving to the left of his goal and Morsy turning it behind before Rotherham could profit.
Despite the sloppy end to the half, the whistle triggered applause from the Town support.
After the all-too-familiar early opposition goal, the Blues quickly gained the upper hand with Burns’s pace against Peltier down the right flank evidently having been spotted as an area which could be exploited.
And exploit it they did with the Welshman scoring twice, assisting once and having come close twice more. Burns and his teammates ought to have plenty of further opportunities after the break.
Nevertheless, it had been a rather disjointed end to the half, while Moore left the field at the end holding his right thigh with Al-Hamadi quickly out to warm up.
Town: Hladky, Clarke, Woolfenden, Burgess, Davis, Burns, Travis, Morsy (c), Burns, Chaplin, Sarmiento, Moore. Subs: Walton, Harness, Al-Hamadi, Jackson, Hutchinson, Luongo, Humphreys, Broadhead, Tuanzebe.
Rotherham: Johansson, Clucas, Eaves, Hugill, Rinomhota, Rathbone (Seriki 36), Peltier, Odoffin, Morrison, Tiehi, Kioso. Subs: Phillips, Humphreys, Cafu, Lindsay, Ferguson, Appiah, Nombe, Wyke. Referee: Keith Stroud (Hampshire).