Leigh Griffiths and Eoin Doyle gave the hosts a two goal lead before Gary Mackay-Steven pulled one back for United.
A patchwork Hibs defence survived a few late scares to hold onto their advantage and win their third league game on the bounce.
The home side's defence was already without the services of Tim Clancy before a late injury to James McPake robbed Hibs of their captain and defensive organiser.
As a result manager Pat Fenlon was forced to shuffle the pack, with Lewis Stevenson coming in at left back and Ryan McGivern shifting over into centre half.
Hibs were almost gifted the lead within the first five minutes. Willo Flood's attempted backpass to Radoslaw Cierzniak was quickly closed down by Griffiths. Curiously, instead of attempting to deposit the ball in either stand, the United keeper opted to pick it up, handing Hibs an indirect free-kick inside the penalty area. Flood atoned for the initial mistake by rushing out to block Griffiths' shot.
You can't keep the diminutive striker out for too long and he notched his twelfth goal in as many league games to give his side the lead in the 18th minute.
There appeared to be little danger when Cairney received possession 30 yards from goal, but the midfielder's reverse through pass was perfectly weighted for Doyle to run onto and his cross to the back post found Griffiths who slammed the ball home off the woodwork.
The first half was scrappy but Hibs were unquestionably the better side, particularly in attack where United looked limp and lifeless in comparison. It was something Peter Houston tried to correct by bringing on Gary Mackay-Steven for the ineffective Mark Millar in the 34th minute.
Despite losing the extra body in the centre, United became more assured in possession following the change and the half, which had threatened to be dominated by Hibs, ended with the away side on top.
Although while United appeared to be an increased threat they hadn't created any chances and Hibs began the second, much like the first, looking the team likelier to score, which they did in the 51st minute.
Cairney, so often the architect for Hibs this season, was the creator again. The midfielder brilliantly nutmegged Keith Watson on the far left side of the penalty area before laying off for Doyle to stroke the ball into the top corner.
It should have represented a commanding position for Hibs but they immediately allowed United back into the game in bizarre circumstances. First Hanlon and then Ben Williams decided against knocking long under pressure deep in their half, and the latter succeeded only in playing it straight to Mackay-Steven who coolly passed the ball around the advanced keeper from the edge of the area.
From then the match was played at a frantic pace with both sides desperate to find the next goal.
It seemed the script was written for former Hearts hero Rudi Skacel to complete the comeback, but the second half substitute saw his close range header ruled out for offside, and soon after the woodwork came to Hibs rescue after the attacker attempted an audacious effort.
With his body turned away from goal Skacel unleashed a first time volley from 20 yards that had beaten Williams but came crashing back off the crossbar.
With three minutes remaining Skacel took one last bite at the cherry, but saw his first time shot, following a Jon Daly knockdown, slice wide of the goal.
Tempers frayed just before full-time with an altercation between Skacel and a couple of Hibs players. And after the completion of the match the Czech responded to the abuse from the Hibs support by pointing to the "51" on the back of his shirt.