The visitors missed a series of first-half chances at New Douglas Park on Saturday and paid for their profligacy in the 33rd minute when Mickael Antoine-Curier sent Dusan Pernis the wrong way from the spot after Prince Buaben had fouled Gavin Skelton.
Battling Hamilton looked to have survived some severe second-half pressure, but in the 83rd minute United substitute Andis Shala, on earlier for Timothy van der Meulen, headed in a Craig Conway cross for what was undoubtedly a deserved leveller.
The home side were given a standing ovation from their fans after the final whistle in recognition of their efforts, but Accies boss Billy Reid will see it as an opportunity lost although it had all pointed to an away win before the game.
Struggling Accies were without an SPL win since beating Motherwell on October 30.
United had won 3-1 at New Douglas Park in the Scottish Cup earlier in the month, but looked no better than the home side in the scrappy opening stages.
But in the 12th minute United should have taken the lead when Scott Robertson escaped down the right and crossed for David Goodwillie, whose leap was good but whose header from 10 yards went wide.
Then, in the 19th minute a mistake by Accies defender Skelton in the box allowed United midfielder Conway to sneak in behind him, but his close-range shot was well saved by Tomas Cerny.
The Hamilton goalkeeper had an escape a minute later when a stretching Johnny Russell failed to connect properly with a Goodwillie cross at the back post when a goal looked certain.
Meanwhile, an edgy looking home side were making little progress although in the 28th minute, with the Taysiders pressed back into their own box for once, the ball fell to Skelton at the edge of the box but he volleyed high over the bar.
But in the 33rd minute the former Gretna player was involved when Hamilton took the lead.
Skelton burst into the box and United midfielder Buaben, with a degree of carelessness, upended him with an awkward challenge leaving Antoine-Curier to open the scoring.
Moments later United missed another good chance when midfielder David Robertson knocked a Paul Dixon cross over the bar from close range.
There was a penalty claim four minutes from the break when Dixon went to ground in the Accies box after a challenge with Jim McAlister, but referee Alan Muir was having none of it.
Former Crewe midfielder Mark Carrington replaced Flavio Paixao at the interval and a clearly buoyed Hamilton started strongly.
Antoine-Curier had the ball in the net a couple of minutes after the restart but was ruled offside to little complaint from the home side or their fans.
United replaced Buaben with Danny Swanson and David Robertson with Stuart Armstrong in the 53rd minute in an attempt to get back level, while for Accies, on the hour mark, Andy Graham came on for the injured Gary McDonald.
But there was little in the way of goalmouth action as a deteriorating game became increasingly tetchy to boot.
Accies made their last substitution in the 65th minute when former United striker Damian Casalinuovo replaced Antoine-Curier.
In the 73rd minute Casalinuovo should have sealed the victory when he left Tannadice defender Sean Dillon for dead inside the United box, but in comical style he miskicked and the ball rolled out for a goal kick.
Minutes later, at the other end, following Dixon's corner from the right, Dillon's overhead kick was hooked off the line by McAlister.
United laid siege to the Accies box in the final stages and in the 83rd minute, from a Conway cross, Shala headed past Cerny, who minutes later made a great point-blank save from Goodwillie to save a point.