Both teams finished the match with 10 men after Hibs midfielder Kevin Thomson and United defender Gavin Gunning raised their hands during a tangle in the 65th minute.
United almost broke the deadlock when Gary Mackay-Steven found David Goodwillie at the back post, and although the ball appeared to get caught under his feet the United striker managed to set up Stuart Armstrong, whose shot was blocked by Robertson's last-ditch block 10 yards from goal.
Armstrong did pounce after 29 minutes with the Hibs defence looking static after his heavy first touch from Ryan Butcher's 40-yard pass. The United winger got his toe on the ball to send it past the advancing Ben Williams.
Hibernian's only effort of note before the break came with a 25-yard strike from James Collins which was beaten away by Radoslaw Cierzniak.
After the interval Goodwillie miscued a header from a Sean Dillon cross while Andrew Robertson found the side-netting after racing forward from left-back as United continued to look more dangerous.
Referee Crawford Allan dismissed Thomson and Gunning after they clashed, and the pair had to be separated again as they left the pitch.
Cierzniak tipped a fierce drive from Liam Craig over the crossbar before Williams denied United substitute Brian Graham after he was sent clear by Ryan Gauld.
Robertson rescued a point, and possibly saved manager Pat Fenlon's job, when he followed up his first attempt at goal to sweep the rebound past Cierzniak from 25 yards with nine minutes remaining.