A Christian Doidge strike meant a first defeat for Dundee United manager Micky Mellon as Hibs fought off the Tangerines at Tannadice.
Doidge broke the deadlock on 65 minutes, smashing high into the roof of the net beyond a helpless Benjmain Siegrist.
The result means United remain in fifth spot and league leaders Hibs continue their perfect start to the Premiership season.
United showed two changes from Saturday’s 1-0 win at Motherwell with debutant Ryan Edwards coming in for the injured Liam Smith and Nicky Clark replacing Logan Chalmers.
The hosts enjoyed the lion’s share of possession in the opening moments before a nasty clash of heads between Jamie Robson and Paul McGinn halted proceedings on six minutes.
In an attempt to intercept Hibs goalkeeper Ofir Marciano’s lofted ball out to his full-back, Robson collided with McGinn as both players went for the ball.
McGinn remained on the pitch but Robson was unable to continue and, after being booked by referee Don Robertson, was replaced by Adrian Sporle on nine minutes.
The Tangerines more-dynamic system caused the visitors a number of problems as the half wore on, with Clark intercepting a Marciano kick out and United dominating the midfield battle.
The first real attempt of the game, though, came from a green jersey as 18-year-old left-back Josh Doig fizzed an effort wide on 19 minutes.
Daryl Horgan was the next to try his luck but fired a left-foot volley against himself and United managed to clear.
The Leith men continued to grow into the match as it crossed the half-hour mark but it was still the Terrors looking most likely to make the breakthrough.
Nicky Clark fired a free-kick over via a deflection on 39 minutes after Ryan Porteous fouled Louis Appere on the edge of the box. From the resultant corner Mark Connolly nodded wide.
A few minutes later Clark curled another set-piece over the bar before Horgan blasted high for the Easter Road side as the first period came to a close.
United were almost in on 54 minutes as Louis Appere tapped home from Sporle’s cutback but the Argentine left sider was adjudged to have been offside when played through by Ian Harkes.
On 57 minutes, the Tangerines fashioned their best opening of the encounter as Harkes lashed on-loan Manchester City kid’s Luke Bolton cutback narrowly wide of Marciano’s post.
Martin Boyle proved a menace for United moments later as he drove into the box and caused a goalmouth stramash begging to be turned home for the opener before Connolly cleared.
It wasn’t long before the Hibees got their goal, however, as Doidge smashed home his second of the season from six yards out to open the scoring on 65 minutes.
Picking up a deflected drive from Doig, the Welsh hitman ferociously drove the ball beyond Siegrist and into the roof of the net.
Harkes saw a low shot comfortably saved by Marciano after strong running from kid sub Lewis Neilson.
Calum Butcher came close with a deflected effort in the final 10 minutes, with Connolly nodding wide from a corner.
Peter Pawlett scooped a glorious opportunity past Marciano’s post as the clocked wound down and the Tangerines failed to level things up.
Dundee United XI (3-5-2): Siegrist (GK), Connolly, Edwards (Neilson 68), Reynolds; Bolton (Chalmers 73), Pawlett, Butcher, Harkes, Robson (Sporle 9); Clark (C Smith 74), Appere.
Subs not used: Deniz (GK), Sporle, Powers, King, Glass and Freeman.
Hibs XI (4-4-2): Marciano (GK), McGinn, Porteous, Hanlon, Doig; Boyle, Gogic, Newell (Hallberg 78), Horgan (Allan 56); Doidge, Nisbet.
Subs not used: Dabrowski (GK), Gray, Murray, Stevenson, Gullan, McGregor and Stirling.
Referee: Don Robertson.