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One goal was enough, a superb second half strike from Kris Doolan.
The Tannadice club were made to regret missing a glut of first half chances.
Thistle had luck on their side, but an improved second half showing brought them three vital points and to within touching distance of the top six.
The result leaves Mixu Paatelainen's men bottom, five points behind Kilmarnock with just six games left.
It was the Tayside club who responded to a vociferous travelling support of 1,909 in a crowd of 4,533.
Ryan Dow had a shot held by Tomas Cerny, and then a great free kick from Paul Paton curled into a dangerous area but could not be cashed in by the United players in the six yard box.
Dow had about four chances in the opening spell, the best of which was a four on three break in which Guy Demel played him in, but he shot over.
Billy McKay was next to nearly take advantage of some comic cuts Thistle defending with a lob just over the bar, swiftly followed John Rankin having a go but being denied by a fabolous save from Cerny.
Rankin went close again with a sizzling 25 yarder just past the post.
At this stage it was King Canute versus the tide.
Against all this, just before half-time Partick should have had a penalty when Gavin Gunning clearly had a grip of Doolan, but referee Andrew Dallas waved play on.
It would have been astonishing had Thistle gone in ahead. It was a miracle that the half finished 0-0.
The injury gods continued to conspire against Thistle right at the start of the second half. Frederic Frans went down with no-one near him and limped off to be replaced by Mustapha Dumbuya, with the home side having already lost Gary Fraser in the first half.
But that tide was turning. There was one fabulous move which ended with Callum Booth volleying just over the bar and there was a new pace and appetite about the home side.
One way or another a goal had to come. And so it did. For Thistle.
Doolan scored his ninth of the season with a magnificent drive from the edge of the box after a sweet build up.
It was joy for Thistle and happiness for Kilmarnock who desperately need United not to close in on their tail.
Partick Thistle leapfrogged Ross County and joined Dundee on 41 points in the race for a top six place and in the process stunned Dundee United in their battle against relegation.