After a quiet start at Firhill, Gary Fraser fired a dangerous shot for Thistle in the 15th minute, which was seen late by United keeper Radoslaw Cierzniak. However, he was still able to beat the ball away to keep the score goalless.
Conrad Balatoni came close on two occasions, but he wasn't able to draw first blood for the home side.
The deadlock was eventually broken by the away side. Farid El Alagui scored his first United goal thanks to some good work by Andrew Robertson, who got past a couple of defenders before squaring for the striker to apply the finish.
A few minutes later, two saves in quick succession from Paul Gallacher denied Farid El Alagui a second goal.
Thistle made a positive start to the second half, with Aaron Taylor-Sinclair's shot trickling wide of the Dundee United goal.
With 15 minutes left to play, the home side equalised. Fraser cut in from the left-hand side of the box and drilled a shot into the United net with the aid of a deflection.
United move a point closer to fourth-place Inverness Caledonian Thistle, while Partick Thistle and Ross County are now 17 points clear of Hearts.