Adam Rooney ensured Birmingham ended their Group H campaign on a winning note - but the Championship club still bowed out of the Europa League.
Former Stoke man Rooney nodded home in the first half from a cross by Nathan Redmond, who hit the post late on.
Birmingham dominated the Slovenian league leaders with David Murphy and Nikola Zigic both going close.
But they were relying on victory by Portuguese side Braga, who could only draw with Club Brugge.
It was tough on Chris Hughton's battlers who dominated their unambitious opponents from start to finish.
Maribor boast a 15-point cushion at the top of the Slovenian top flight and eliminated Rangers from Europe back in August.
Yet they arrived in Birmingham with just one point in Europe after conceding 14 times in their opening five group games.
And they found themselves on the defensive from the start as Birmingham, who made nine changes to the side which defeated Doncaster at the weekend, settled quickly.
Redmond, the exciting 17-year-old winger, teased and tormented the visitors' defence and deservedly received a standing ovation when he was substituted in the closing stages.
The teenager was at the heart of his side's best attacks and it was his first-time flick which presented Zigic with a chance which keeper Jasmin Handanovic saved comfortably.
Murphy found the roof of the Maribor net with a deflected free-kick in the 13th minute, while Jovan Vidovic headed just wide from a corner in a rare Maribor attack.
Birmingham got the breakthrough their attacking play deserved when Rooney headed home from close range in the 24th minute - man-of-the-match Redmond supplying the cross for the Dublin-born player to score.
As good as Redmond was, Zigic was poor.
The Serbian striker was presented with a fine chance to double the lead after bursting through the Maribor defence before half-time, but his finish was disappointing.
Then the buoyant mood around St Andrew's was punctured when news filtered through that 10-man Braga had fallen behind in Belgium.
And the mood of Birmingham fans did not improve when Arghus was booked for an ugly challenge on Redmond with the Maribor player fortunate not to be sent off.
News of a Braga equaliser lifted the crowd - as well as Hughton's side.
Murphy had a goal-bound shot blocked by Aleksander Rajcevic while Curtis Davies narrowly failed to direct Redmond's corner into the net.
With Birmingham heading out of Europe, Zigic had a header deflected over the bar after more good wing play by the industrious Redmond.
And Redmond capped a delightful performance by rattling the Maribor post with a terrific volley four minutes from time as Birmingham bowed out on a high.