Dan Potts scored the only goal of the game as Luton's 1-0 win increased the pressure on Birmingham boss Aitor Karanka.
Potts' goal - on his 150th league appearance for the club - sentenced Blues to an 11th home game without a win, less than 24 hours after chief executive Xuandong Ren gave Karanka a vote of confidence.
Defeat left Birmingham with one victory in their last 12 Sky Bet Championship outings, with three points out of 36 to lie second from bottom of the table, a point below the safety line.
The visitors edged a forgettable encounter, with defences largely on top and goalmouth action thin on the ground as Blues extended their record as the second tier's worst home team, with nine points from 45 at St Andrew's.
Luton, who ended a three-match winless spell in the Championship to climb to 14th, created the first chance when James Collins beat George Friend to a long pass from Tom Lockyer and lobbed the ball into the side-netting.
The Hatters threatened again, this time from a corner swung in by Kiernan Dewsbury-Hall, when Matty Pearson's towering header was held by goalkeeper Neil Etheridge.
Blues' only chance of the opening half-hour was a poor shot by Jeremie Bela that bounced well wide after Kristian Pedersen's cross was headed back into the danger area by Ivan Sanchez and Lockyer touched the ball into the winger's path.
Luton had been the better side and took a deserved lead in the 31st minute.
Birmingham failed to deal with a long throw-in from Harry Cornick on the left, Etheridge made a superb instinctive save to block Collins' close-range shot on the turn and Potts headed home the loose ball.
It was Potts' first goal since October 23, 2019 and only Luton's seventh away goal of the season.
Luton remained on top and Jordan Clark forced Etheridge to tip away a left-footed drive before Potts headed wide from Dewsbury-Hall's corner.
Birmingham's first effort on target came in the 52nd minute when Gary Gardner's stooping header flew straight at goalkeeper Simon Sluga.
The home side made a triple substitution in the 69th minute in an effort to drag themselves back into the game.
Lukas Jutkiewicz, Sam Cosgrove and Ivan Sunjic replaced Scott Hogan, Gardner and Alen Halilovic, who had made his first home start.
But it was Luton who created the next chance as defender Sonny Bradley sent an overhead-kick wide after Blues struggled to deal with another long throw-in from Cornick.
Luton reminded Birmingham of their set-piece threat when Potts' flick was deflected over by Yan Valery from Pelly-Ruddock Mpanzu's corner.
What the managers said...
Birmingham's Aitor Karanka: "The effort concerns me because we knew Luton were good at long balls and second balls and when they won every second ball it means they had more effort than us.
"We showed the players the set-pieces and throw-ins (before the game), yet they scored the goal from one throw-in - every single corner they headed the ball. So that is why I talk about the effort."
Luton's Nathan Jones: "I felt it was deserved. You're never totally comfortable but I felt we restricted them to very little. It was a scrappy game that lacked a bit of quality but I felt any chances that were had were had by us.
"We were a little bit disappointed not to go in further ahead. We then had to do the basics and I thought we did them really well in the second half. It's vitally important you keep moving forward - we had a tough January with four away games on the spin. It's nice now to back up our performances with points because we've started the month well, unbeaten and taken four points. We had enough of the game to have won and we did."