David Goodwillie and Brian Graham prevented United falling to a fourth successive defeat after they had trailed to a Liam Craig brace.
Goodwillie stabbed the ball in from close range following some cleaver play from Graham to give United some hope.
Graham then nipped in behind the Hibs defence to stick the ball past goalkeeper Ben Williams in the final minutes of regulation time.
Craig stuck seven minutes before the break when Rado Cierzniak's kick-out was instantly returned by Paul Heffernan and midfielder got in behind the United defence to blast home.
Hibernian doubled their advantage as Craig (61) confidently dispatched his spot-kick after Jon Souttar had pushed James Collins to concede the penalty.
The visitors had the best of the opening half and former Hibs midfielder John Rankin came to United's rescue on 16 minutes when he cleared Paul Hanlon's header off the line.
Dundee United responded when Williams had his palms stung by Nadir Ciftci after a free-kick was rolled to the striker outside the penalty area to shoot towards goal.
Four minutes later Cierzniak tipped a Michael Nelson's header over the bar before the United keeper saved a shot from striker Collins after half-an-hour.
In-between those efforts Gary Mackay-Steven tapped the ball into the net after Cifti's through pass was shanked by Williams leaving the winger with an open goal, but Ryan Gauld was adjudged offside in the build-up.
United created another opening just before the break with a lightening break but Williams got down to save the shot from Mackay-Steven.
Williams denied United with 15 minutes remaining as a shot from Mackay-Steven came off a defender, but further drama was still to come.