If they had won at the Firhill Stadium in Glasgow on Sunday, United would have gone top on goal difference, albeit for just half an hour until the end of the Aberdeen match, with Celtic not playing until Monday.
Instead, they drop to fourth with Hamilton leapfrogging them thanks to their victory at St Johnstone.
United appeared a little weary in the first half, following their 6-2 New Year’s Day derby win over Dundee, whereas Partick were fresher, having had their first game of 2015 against Celtic postponed due to a waterlogged pitch.
Jackie McNamara’s men nevertheless started the brighter, with Thistle keeper Paul Gallacher having to get down smartly in the first minute to save from midfielder Gary Mackay-Steven after he was clear through.
Within 10 minutes, Mackay-Steven had opened the scoring, latching on to a neat through-ball from Turkey-born striker Nadir Cifti to slot the ball past Gallacher.
Despite being hit by injuries, Alan Archibald’s Partick side pressed forward seeking the equaliser and a quarter of an hour later, Thistle captain and man-of-the-match Ryan Stevenson got on the end of a Gary Fraser corner to head his fifth goal of the season.
Moments later, a smart first-time volley from Kris Doolan nearly put them ahead, forcing a good save from Radoslaw Cierzniak in the visitors’ goal.
And it was Doolan who did give Partick the lead in the 32nd minute, running late into the box following a cross from Fraser to guide it past Cierzniak.
With their tails up, Thistle forced another few good saves from Cierzniak and went very close minutes before the end of the first half, Declan McDaid magnificently setting up Doolan who couldn’t finish and then saw Fraser’s point blank effort blocked by the United keeper.
After half-time, however, United were the more forceful and, shortly after bringing on their third substitute, Mackay-Steven went on a long solo run. The ball fell to Cifti who fired home the 73rd-minute equaliser.
The final quarter of an hour was mainly one-way traffic as United sought a winner, but Thistle’s young defence held firm to earn a well-deserved point.