In an eventful game, Nadir Ciftci and Gary Mackay-Steven both erred from the spot, yet the former put his tame effort behind him by opening the scoring in the 43rd minute.
Hibernian equalised almost immediately through Jordon Forster, only to then concede further goals to Gavin Gunning and Farid El Alagui in the second half either side of Mackay-Steven blazing a penalty over the crossbar.
The hosts' misery was also compounded by the 72nd-minute dismissal of Tom Taiwo for a second bookable offence.
Terry Butcher's side remain seventh and face a battle to secure a top-six finish, while United move up to fourth.
After seeing a penalty saved midway through the first half, Ciftci bounced back by cutting in from the right and finishing calmly.
Forster was gifted a leveller when visiting goalkeeper Radoslaw Cierzniak flapped at a corner, but United restored their advantage 11 minutes after the interval when Gunning produced a towering header to register his third goal in two games.
Mackay-Steven's dismal effort from 12 yards was followed by Taiwo seeing red, but there was still time for El Alagui to make it 3-1 with a near-post finish from Andrew Robertson's left-wing cross.
‘Scoring in a World Cup is like winning the title – can you imagine millions of people celebrating something you did? It’s insane and made me very proud’: Brazil legend explains how much 2002 goal meant to him
'He already had the ability but didn’t use it because he was afraid to shoot – I said, "You’re a player who has to decide games – you have to take risks, mate"': Liverpool star was forced to become confident by team-mates
