Hibs recorded their fourth successive victory but only by the skin of their teeth.
Twice in the final two minutes Dundee United hit the woodwork as Hibs clung on to the three points.
Dave McCracken sent a header against the crossbar after a corner from substitute Steve Carson and then deep into injury time Steven Thompson cracked a shot against the bar with Nick Colgan beaten.
Ian Murray supplied what proved to be the match-winning goal with a stunning strike early in the second half.
He took the ball from just inside the United defence before unleashing an unstoppable 25-yard right-foot shot.
The goal was fit to win any game but United can count themselves unlucky not to take something from Easter Road.
But manager Alex Smith was frustrated at the fact his team did not start playing until they were two goals behind.
Substitute Charlie Miller changed the pattern of the game when he came on a minute after Murray's goal.
The chunky midfielder was denied on one occasion by a superb save from Colgan as he took a firm grip on the midfield.
United pulled a goal back on 75 minutes when Carson cut the ball back for Thompson to sidefoot the ball home, but Hibs survived at the death as they enjoyed their best spell for over two years.
There was nothing in the first half to suggest such drama at the death. Both sides lacked imagination going forward and chances were few and far between.
Hibs took the lead after 28 minutes when Garry O'Connor shrugged off the challenge of Warren Cummings to score from close range after Murray had provided a looping cross.
Paco Luna should have made it two shortly before the break but he sent a six-yard header wide of target.
But when Murray scored early in the second half it looked to be all over before United fought well to at least assure the game finished on a knife-edge