A devastating first-half display blew the visitors away, as Hibernian kept up the pressure on third-placed Rangers.
Riordan celebrates his early strike
The home side opened the scoring early on when Derek Riordan cut in from the left-hand side, before shooting low past Craig Samson.
Alan Archibald then headed into his own net, before Chris Killen made it 3-0 shortly after when he skipped past Garry Kenneth and slotted home.
Substitute David Goodwillie grabbed a late consolation from close range.
Hibernian started the match without Moscow-bound Garry O'Connor, who was sitting in the stand.
The Easter Road outfit got off to the perfect start when Kevin Thomson fed Riordan on the left, who cut inside two United defenders and drilled a low right-footed shot into the bottom corner.
United almost hit back a few minutes later when ex-Hibs player Grant Brebner saw a dipping long-range half-volley graze the top of Simon Brown's bar.
Samson then comfortably collected a Riordan free-kick after Kenneth's foul on Killen.
United had another great opportunity soon after but Mark Kerr should have done better from six yards, when his mis-kick drifted wide.
However, all their work was undone when Archibald headed Riordan's teasing cross into his own net.
United looked to quickly get back in the game, but again shot themselves in the foot by conceding a third, as Hibs threatened to run riot.
Riordan's long ball over the top looked harmless, but Killen was on to it in a flash and showed great physique to win the ball ahead of Kenneth.
After outwitting the young defender, the New Zealand international drove a close-range angled shot across Samson and into the far corner.
United boss Craig Brewster was unimpressed with the opening half from his team and withdrew David Fernandez and Stuart Duff for Colin Samuel and David Robertson at the start of the second period.
The move sparked some urgency in the visitors and Barry Robson brought a smart save from Brown at his near post on 48 minutes.
David McCracken should have pulled one back from Robson's free-kick but glanced a free header wide, before Paul Dalglish brought out a flying save from Samson with a long-range effort at the other end.
United missed their best chance of the game when Robson picked out Samuel in space at the back post but the Trinidadian could only prod the ball at Brown's legs.
Riordan and Steven Whittaker were off target with Hibs efforts before a smart close-range save from Samson denied the onrushing Ivan Sproule on 81 minutes.
United manfully battled on and claimed a consolation when 16-year-old substitute David Goodwillie forced home his first goal for the club two minutes from the end, after first Samuel had hit the bar and then Robertson the post.
Hibernian: Simon Brown, Whittaker, Smith, Caldwell, Murphy, Stewart (Konde 56), Thomson, Glass, Riordan, Killen (Fletcher 75), Dalglish (Sproule 61). Subs Not Used: Malkowski, Hogg, Konte, McCluskey.
Goals: Riordan 6, Archibald 25 og, Killen 33.
Dundee Utd: Samson, Kenneth, Archibald, McCracken, Mair, Kerr, Brebner, Robson, Duff (Robertson 47), Miller (Goodwillie 86), Fernandez (Samuel 45). Subs Not Used: Abbot, Gardiner, McInnes, Gibson.
Booked: Robson, Kerr, Brebner.
Goals: Goodwillie 89.
Ref: B Winter