Farid El Alagui gave the away side a first-half lead before Fraser's second-half strike earned the home team a share of the spoils.
It was a lively start from both sides who have both struggled for form of late.
Fraser had a shot from range saved by United's Radoslaw Cierzniak after 10 minutes only for Nadir Ciftci to have a long-range effort saved by Paul Gallacher at the other end a minute later.
Conrad Balatoni almost gave the home side the lead midway through the first half but his right-footed effort struck the post to Cierzniak's relief.
Relief turned to ecstasy in the 29th minute when El Alagui smashed the ball into the top-right corner to give the visitors a deserved lead.
El Alagui should have extended United's lead shortly after but was twice denied from close-range by Gallacher
Lyle Taylor and Prince Buaben both mustered efforts for the home side as the half drew to a close without managing to trouble Cierzniak.
Dundee United looked in control as he second half progressed with Stuart Armstrong twice going close.
But with 15 minutes to go Thistle got an unlikely equaliser following a corner conceded by Gary Mackay-Steven.
Fraser fired the ball home from a tight angle after receiving the ball back from a corner which he took.
John Rankin had two chances to earn a late victory for Dundee United but he was unable to find the target on both occasions as the away side had to settle for the draw.