Goals from Leigh Griffiths and Eoin Doyle put Hibs in the driving seat before Gary Mackay-Steven pulled one back for United, who were unfortunate not to earn a share of the spoils.
Griffiths (19) opened the scoring with a spectacular volley into the roof of the net after a slide-rule pass from Paul Cairney put Doyle through to deliver a pinpoint cross to the back post.
Cairney was again the creator as Hibs doubled their lead on 53 minutes when he put the ball through Keith Watson's legs and laid a pass back for Doyle to rifle home from eight yards.
But United were given a lifeline two minutes later as a mix up between Paul Hanlon and Ben Williams resulted in the keeper's heavy touch falling to Mackay-Steven and he passed the ball into the net from 20 yards.
Hibs had dominated the opening period with Griffiths twice testing United from free-kicks and Hanlon just failing to connect with another set-piece from the winger just after the break.
United's goal changed the flow of the game and Hibs got off the hook when Rudi Skacel ghosted into the box to meet a dipping delivery from Flood to send his header into the corner of the net, only to be denied by an erroneous offside flag.
Skacel then volleyed off the woodwork from 25 yards after Jorge Claros headed the ball out of the penalty are at a United corner and Williams clutched a powerful Gavin Gunning header under the bar
There were two further chances for Skacel but the United substitute snatched at both, meaning there would be no dramatic late goal for his new team for the third game in succession.