Natasha Dowie put the Belles ahead from close range early on but Freda Ayisi's header drew the hosts level.
Birmingham were in front before half-time thanks to Melissa Lawley's deflected strike and they held on for victory in a scrappy second half.
Defeat leaves Doncaster bottom of the table and without any points from their first three league games of 2016.
The Belles' best chance for an equaliser came when Dowie fired across the box but Katrin Omarsdottir could not quite get a touch to turn the ball goalwards.
Birmingham are up to fifth in the table, six points behind leaders Chelsea and second-placed Manchester City.
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Birmingham midfielder Jo Potter: "We needed that result after losing our first two league games - we didn't play badly in either of them, but tonight was a must-win for us.
"We had to stamp our authority on this game, and after going behind that's exactly what we did.
"We didn't panic after conceding, we kept our heads, kept believing and once we'd got the equaliser I always felt we would go on to win the game.
Doncaster Rovers Belles goal scorer Dowie: "We gave away two sloppy goals. If teams open you up and score good goals against you that's one thing, but both of those were preventable.
"We can't carry on conceding goals like that, we have to keep them out and take our chances at the other end.
"We came back into the game in the second half and in the end I think a draw would have been a fair result, but we just couldn't get an equaliser.
"We'll learn from this, though. We're a new team in the top flight and we're going to be the underdogs in games, but we'll improve and we'll be competitive."
Birmingham City Ladies earned their first win of 2016 as they came from behind to beat Doncaster Rovers Belles.