Tannadice skipper Jon Daly gave his side a 13th-minute breakthrough and a second on the counter-attack from Craig Conway only three minutes after the interval clinched the win before substitute Johnny Russell put the icing on the cake with a late third.
The defeat leaves Colin Calderwood's outfit with only three victories in 17 games during his sorry tenure.
Now without a goal in seven outings, the Easter Road men lie in 11th spot, precariously just two points above bottom side Hamilton.
Calderwood handed debuts to new signings Martin Scott, who joined from Ross County this week, and Liverpool youngster Victor Palsson as he made four changes in an ultimately unsuccessful bid to find a solution to his team's dire sequence without a victory.
United counterpart Peter Houston made three key switches of his own, with skipper Daly and Scott Robertson returning from suspension and David Robertson earning a start.
United were afforded the first sniff of the goal after just three minutes as the Hibs defence was caught flat-footed by Craig Conway's deep cross from the left flank - and it was a theme that was to continue throughout the 90 minutes.
However, on this occasion, David Robertson, stealing in on the blind side of Callum Booth, could not control his volley enough to get it on target.
Hibs midfielder Liam Miller then had two chances to give the visitors the goal they had not managed in six previous games in 2011.
The former Manchester United and Celtic player had a 25-yard drive blocked before, in the next attack, he hit the side netting following a turn at the apex of the six-yard box.
The Easter Road men then spurned a golden opportunity to make the breakthrough after only 10 minutes.
Paul Hanlon's free-kick was headed on by Colin Nish but Danny Galbraith blasted his volley over from eight yards out when he should have scored.
That miss proved costly when United broke the deadlock just three minutes later.
A long cross-field pass was knocked into the box by Keith Watson and flicked on by David Robertson to allow Jon Daly to bundle his shot past Graeme Smith in the Hibs goal.
Daly had a second chance in the 25th minute but his header from Conway's cross slipped wastefully wide.
United continued to cause Hibs problems with seemingly routine crosses into the box but, although the Tannadice outfit continued to enjoy the upper hand, Hibs did manage to work their way into a number of promising situations.
However, too frequently the final ball lacked accuracy or, as in Nish's header from Miller's free-kick, the end product was also missing.
Given the Edinburgh side's lack of goals since the turn of the year, the second in this match was always going to be crucial.
United almost grabbed it five minutes from the interval but Scott Robertson flashed his drive from the edge of the area past Smith's right-hand post.
And only three minutes into the half they finally doubled their lead with the simplest of goals.
Goodwillie's pass over the top caught the Hibs defence sleeping and Conway raced away from the covering Francis Dickoh to fire a superb effort beyond Smith's despairing dive from just inside the box.
Hibs almost quickly grabbed a lifeline six minutes later as United defender Garry Kenneth gifted possession to the visitors.
Scott fed David Wotherspoon midway inside the home half but after working his way into the box the midfielder saw his shot blocked by keeper Dusan Pernis.
But there should have been no way back for Hibs in the 63rd minute as United wasted a golden opportunity to add a third.
Goodwillie exposed a gaping hole at the centre of the visitors' defence with a perfect pass to David Robertson but the midfielder blasted high over the bar when he should have scored.
Hibs boss Calderwood threw on strikers Darryl Duffy and Kurtis Byrne and handed new recruit Matt Thornhill his debut with a last throw of the dice 18 minutes from time, but it was difficult to see where the inspiration for a late comeback would come from.
And, with only 10 minutes remaining, United showed the visitors the way to goal as they clinched a comfortable win with a third.
Hibs somehow survived an almighty goalmouth scramble following Conway's corner but, when the ball was returned by the winger, Russell knocked home after Smith had initially saved the substitute's header.
Thornhill and Palsson brought saves from Pernis as Hibs finished the match on the attack but they could not even find a morale-boosting late consolation.