It was a win which, on the balance of play, the visitors deserved, yet the Tangerines had their chances and manager Craig Brewster must be desperately seeking a striker to give him more muscle up front.
It was United who started the more sprightly with Noel Hunt coming close with only two minutes on the clock, finishing off an excellent three-man move. The striker connected with Craig Conway's curling cross but unfortunately saw his close-range effort slide past the post with the goalkeeper stranded.
The Terrors then had a strong shout for a penalty denied when Rob Jones brought down Hunt in front of referee Craig Thomson.
Hibs' first serious chance came in the 28th minute when Abdessalam Benjelloun jinked to the edge of the box only to see his goal-bound shot deflect off Alan Archibald's boot and skim over the bar with Derek Stillie stranded.
After two close calls when United were wrongly ruled offside in good positions, Merouane Zemmama weaved and danced his way past four defenders before shooting wide from 16 yards.
The visitors should have taken the lead in the very next minute when defender Jones blasted over from only two yards.
It was not all one way. With five minutes remaining before the break only a fantastic low one-handed stop from Zbigniew Malkowski prevented Collin Samuel's low drive bursting the net.
And to end an entertaining first period, Scott Brown ran fully 40 yards before firing an excellent 20-yard shot which Stillie did well to hold.
Seven minutes after the break Hibs were gifted the lead. A long ball from Shelton Martis caught the United central defenders, David McCracken and Archibald sleeping to allow Chris Killen to run straight through and thump the ball past Stille from 16 yards.
This gave the visitors confidence and they really began to take control of the game. Benjelloun almost made it two in the 63rd minute but a wonderful block by Stillie's foot diverted the ball round the post
Samuel could have equalised in the 66th minute but he woefully headed wide from in front of goal.
United player-boss Brewster brought himself on and only a wonderful save from Malkowski prevented him levelling from Christian Kalvenes' cross.
The match was sealed in the 81st minute when substitute Dean Shiels delightfully chipped the ball over Stillie after the keeper parried a stinging drive from Benjelloun.
United collapsed and Ivan Sproule added a third just before the whistle.