Manager Nathan Jones made two changes from the team that beat Barnsley 1-0 in midweek, Allan Campbell coming into midfield in place of the injured Henri Lansbury, whilst Harry Cornick partnered Elijah Adebayo up-top, in place of Cameron Jerome who was among the substitutes.
Fred Onyedinma was back in the matchday squad after being forced off against West Brom, whilst there was a first home league start for Peter Kioso in defence.
Birmingham started on the front foot, Marc Roberts cross from the left finding centre-half partner Kristian Pederen's head in the opening two minutes, but it flew safely past Simon Sluga's far post.
Roberts was first to be booked for a foul on Cornick, with Bree's free-kick causing concern in the Birmingham six-yard box, but neither Elijah Adebayo or Tom Lockyer could take advantage as Matija Sarkic struggled to clear in the fifth minute.
The visitors had the lead a minute later when Roberts met Jeremie Bela's near-post corner with a firm header that gave Sluga no chance.
Town spurned a chance to level on 15 minutes, when Lockyer brought the ball out of defence and set Cornick free, but his floating cross from the right was fractionally too high for Admiral Muskwe coming in at the far post.
Midway through the half Bell tried his luck from 35 yards, his drive skidding off the greasy surface and making it difficult for Sarkic to hold on to, but Lockyer's attempt to force home the rebound was too high.
It was 2-0 in the 26th minute when Bell's header clear from a Bela cross dropped at Tahith Chong's feet. The Manchester United loanee picked out an unmarked Scott Hogan to head past Sluga once more.
Jones made an immediate switch, taking off Peter Kioso and reverting to a flat back four, with Glen Rea coming in to anchor the midfield.
Adebayo was soon causing problems down the left, bursting past Roberts and cutting a low cross back but neither Cornick or Muskwe could get a finish on.
Rea was soon into ref John Busby's notepad for a trip on Ryan Woods, but he was putting himself about and triggering a flurry of attacks, without the Hatters creating and real chances of note.
It was Sluga who was called into action again three minutes into time added on to push a shot from Chong away, before Pedersen fired into the side-netting as the Town struggled to clear another set piece just as Busby prepared to blow the half-time whistle.
Jones made a second change at the break, taking off Campbell and replacing him with Fred Onyedinma. Within two minutes, however, things had gone from bad to worse as a Bree corner from the left was cleared at the near post, Mpanzu miscontrolled and Chong carried the ball forward at pace.
The Blues' wideman beat Bell on halfway and was clean through on Sluga as Mpanzu slid in to block his shot with a perfectly timed challenge, only for the ball to roll straight into Hogan's path, and the City forward rolled it into an empty net.
Onyedinma went close with an overhead-kick in the 57th minute, after Cornick dug out a cross from by the right corner flag and Adebayo nodded back across goal.
It was Cornick's last involvement, Jones introducing Cameron Jerome in his place, but it was Chong who was soon warming Sluga's palms again at the other end, with a low shot from outside the box just before the hour.
Bree got in on the right side of the City area in the 67th minute, Adebayo finding the full-back's run but his cross-shot was turned behind at the near post by a combination of Muskwe and Roberts, referee Busby deeming the Town man had the last touch.
Bree asked a question again in the 74th minute, whipping in a free-kick after Rea had been fouled by Chuks Aneke out on the left, but unfortunately Adebayo couldn't get a touch as the ball travelled through the penalty area.
With just under a quarter of an hour to go, Sluga released Onyedinma with a long kick, and after forcing Harlee Dean into an error, the winger fashioned a shooting opportunity, but once again his left-footed effort flashed across the face of goal.
Aneke went close to adding to the visitors' advantage, only for Sluga to stand strong, but it wasn't long before substitute Gary Gardner did, curling into the top corner with 20-yard shot from the angle of the area with five minutes to go.
It was five in the 88th minute when Aneke scrambled one in from close range to complete a miserable afternoon for the Hatters.
Goals:
City - Roberts 6, Hogan 26, 47, Gardner 85, Aneke 88
Att: 10,014 (1,006 away)