El Alagui finished off a good United move just before the half-hour but Fraser levelled in the second half after his corner was cleared back to him.
Both sides came into the game in wretched form, Partick without a win in four and Dundee United without a victory in their last six matches.
This was reflected in the starting line-ups, with Thistle boss Alan Archibald making three changes to the side that earned a goalless draw at St Mirren last week.
Deadline-day loan signing and former Dundee United midfielder Prince Buaben was pitched straight into the side for Aaron Muirhead and with Chris Erskine unable to play against his parent club, Fraser came in alongside Christie Elliot, who replaced James Craigen on the Jags' right.
Partick's other loan capture on deadline day, West Ham's George Moncur, had to settle for a place on the bench.
Jackie McNamara also put his faith in loan signing Curtis Good, the Newcastle United youngster slotting in at the back alongside the returning John Souttar. Mark Wilson replaced Keith Watson, and Stuart Armstrong and Nadir Ciftci also returned to the side.
The home side were the first to threaten after 10 minutes, some lovely link-up play between Kallum Higginbotham and Lyle Taylor on the left seeing the ball being worked inside to Fraser, whose low drive from 20 yards had to be turned away smartly by United goalkeeper Radoslaw Cierzniak.
Buaben was taking time to adjust back to the frantic pace of the Scottish game, and he was booked for hauling down Ciftci after 17 minutes after already receiving an earlier warning from referee Willie Collum for a late challenge on Souttar.
United then had a penalty claim as Armstrong was sandwiched between Buaben and Jordan McMillan as he drove into the area, the Arabs captain left furious as referee Collum waved away his appeals.
Almost immediately Thistle charged up the other end and won a corner, Higginbotham's delivery finding the head of Conrad Balatoni who directed the ball just wide of the right-hand post.
Another driven corner by Higginbotham caused more havoc in the United box, and again it was Balatoni who had the opportunity, his right foot effort squirming agonisingly on to Cierzniak's post.
The visitors had rarely been seen as an attacking force until this point, however they served Thistle with a warning when the excellent Andrew Robertson cut inside from the left and tested Gallacher with a right-foot curler from the edge of the area.
Partick failed to take heed though, and on 29 minutes United were in front. Gary MacKay-Steven showed great feet to evade two challenges and played the ball inside McMillan to release the marauding Robertson up the left wing. The full-back skipped around Lee Mair and squared for the unmarked El Alagui to finish from eight yards.
The visitors started to take control of proceedings and after Stuart Bannigan had been booked for a crude foul on Mackay-Steven on 28 minutes, the United winger set up another great chance for El Alagui.
His clever flick found the on-loan Brentford striker inside the box, and he drew a great double-save from Paul Gallacher before the ball was eventually scrambled clear.
Thistle centre-half Balatoni then decided to take matters into his own hands to bring the home side back into it, driving forward from the back through the United midfield before slipping a clever ball through to Taylor. With just the goalkeeper to beat, the striker could only drag his right-foot effort wide of the target.
Thistle started the second half on the front foot, and again a Higginbotham corner caused concern for United, Aaron Taylor-Sinclair eventually getting a shot away that was desperately blocked before the returning cross from Higginbotham was sliced just wide by a United foot.
Partick were still vulnerable to the counter attack though, and Armstrong should perhaps have done better than sweep the ball wide from around the penalty spot after a fine break.
Alan Archibald made his first change after 58 minutes, Stephen O'Donnell replacing McMillan at right-back, and Higginbotham succumbed to the knee injury that had been troubling him a minute later, being replaced by Kris Doolan.
Wilson then found his way into the notebook for a foul on Taylor-Sinclair as the full-back tried to get beyond him on 60 minutes.
The home side continued to press for the equaliser, and their dominance pressed United manager McNamara into a change of shape after 63 minutes, bringing on Ryan Gauld for Ciftci to bolster numbers in midfield and replacing goalscorer El Alagui with Brian Graham at the same time.
It did little to stem the tide of Thistle attacks however, and Partick eventually got their reward that their second-half display merited with the equaliser after 75 minutes.
It was little surprise that it came from a corner as the United defence had struggled to deal with Thistle's set-pieces all day, and when they could only clear Fraser's delivery back to his feet, the midfielder cut inside before firing a deflected drive past the helpless Cierzniak.
McNamara responded by sending on Ryan Dow for Armstrong after 77 minutes, and they should have taken the lead again after a corner was helped back into the area to Graham. With Thistle goalkeeper Gallacher stranded, the substitute got too much on his header and it dropped just over the bar.
The tiring Buaben was replaced by James Craigen with 10 minutes remaining, and Taylor was booked for hauling back Souttar in the final minute. Rankin fired the resulting free-kick just wide, but neither side could go on to find a winner.