However, despite success over Preston North End and Queens Park Rangers, the two clubs still sit in 21st and 19th position in the standings respectively.
Match preview
Of all the teams to end Preston's long-standing clean-sheet record, Birmingham would have been the undisputed last pick of the majority of people given their issues in front of goal.
That said, this is the Championship and anything can happen, which it did as Maxime Colin netted the only goal of the game in the 16th minute.
Such has been been Blues' poor start that they have only moved outside of the relegation zone on goal difference, but John Eustace will now feel that they have momentum on their side.
Their lack of ruthlessness in the final third remains an issue with Scott Hogan the only player to contribute more than one goal or assist in the Championship during Birmingham's opening eight matches.
However, their defensive performances are keeping them in matches, and there will be confidence that they can overcome a Swansea side in a similar position.
With Michael Obafemi seemingly annoyed that a transfer to Burnley did not materialise, it remains to be seen how the forward will be reintegrated back into the starting lineup.
Nevertheless, Joel Piroe, another player who had been heavily linked with an exit this summer, has stepped up in the last two games to help the Swans to four important points.
Although the Dutchman is yet to replicate his form from 2021-22, the signs are there that he is nearing that kind of output by scoring in his most recent three outings.
However, it will take a collective effort for Russell Martin's team to move further away from the bottom three, and they will be hoping to build on losing just one of their opening four league matches on their travels.
Birmingham City Championship form:
Swansea City Championship form:
Team News
Barring any injury issues, Eustace could stick with the same Birmingham XI from the victory over Preston.
However, he does have alternatives available to him with Hannibal Mejbri and Jordan James both pushing for opportunities in midfield.
Even if he has recovered from injury, Przemyslaw Placheta may have to make do with a spot among the replacements.
Should Obafemi return to the fold for his game, he could only feature on the substitutes' bench with Oliver Cooper making a positive impression against QPR.
Matthew Sorinola will hope to retain his spot on the right flank, while Wolverhampton Wanderers loanee Luke Cundle will likely have to stay patient before making his first start.
Birmingham City possible starting lineup:
Ruddy; Sanderson, Roberts, Trusty; Colin, Bielik, Chong, Graham; Bacuna; Hogan, Deeney
Swansea City possible starting lineup:
Fisher; Naughton, Wood, Cabango, Manning; Sorinola, Grimes, Allen, Paterson; Obafemi, Piroe
We say: Birmingham City 1-1 Swansea City
All things considered, both teams should be pushing hard for all three points after a mixed start to the campaign. However, they will each see the value in a draw, and a low-scoring affair appears to be the most likely outcome.