Gary Neville's first Premiership goal for three years put United three points behind Chelsea with a game in hand, and kept Leicester in the bottom two.
Only 90 seconds had been played when Roy Carroll's weak clearance fell straight to Muzzy Izzet 10 yards out but he shot wide of the corner flag.
Leicester continued to impress as United struggled in the first period.
But Neville slammed home from close range after Cristiano Ronaldo's effort was only partially cleared.
Key United pair Roy Keane and Ruud van Nistelrooy were not fit to return, while Leicester chose to go into the match without a substitute goalkeeper.
United had to wait until 15 minutes for their first chance, a patient build-up seeing Paul Scholes find Neville, whose chip over the defence was controlled by Louis Saha, but his shot on the turn was sliced high and wide.
Nicky Butt had to be alert to hack away a dangerous cross from Jordan Stewart, while Saha ghosted past two challenges into the box but was smothered by Ian Walker.
The former Spurs keeper also had to keep out a dipping 25-yard volley from Butt, while United's first half frustration was summed up when Diego Forlan sent a well placed free-kick straight into the wall.
Moments before the break Leicester spurned another golden opportunity, Marcus Bent heading an Izzet free-kick wide from six yards.
2 mins Izzet scuffs wide for Leicester
44 mins Bent header off target for Leicester
59 mins Neville fires in Man Utd winner
United started strongly after the break and Ronaldo's stinging goalbound drive cannoned off the head of Billy McKinlay.
Riccardo Scimeca made an important interception to put David Bellion's cross behind with Ronaldo poised at the back post.
Just before the goal, Walker parried a deflected shot from Ronaldo and Paul Scholes dallied over the rebound, but moments later Ronaldo fired in again and Neville made no mistake from the loose ball.
Scholes tested Walker again with a shot on the turn, but at the other end another Izzet free-kick caused more problems as Carroll failed to collect.
Ben Thatcher, his shirt covered in blood after his nose was knocked in a challenge with Bellion, blasted an invitingly placed central free-kick 25 yards out high into the stand.
Following a storming run from Wes Brown, Scholes went close again with a left-foot attempt that Walker tipped over.
McKinlay gave United a late scare when his low drive from long range bounced awkwardly just in front of Carroll, but the Northern Ireland international got safely behind the ball.
Ronaldo continued to dazzle with his array of skills, a low curling shot heading for the bottom corner until Walker's outstretched fingertips turned it round the post.
Man Utd: Carroll, Gary Neville, Brown, Silvestre, O'Shea,
Ronaldo, Butt, Scholes, Bellion (Djemba-Djemba 83),
Forlan (Fletcher 57), Saha.
Subs Not Used: Howard, Solskjaer, Giggs.
Leicester: Walker, Thatcher, Dabizas, Heath, Scimeca, McKinlay,
Izzet, Freund (Gillespie 66), Stewart (Scowcroft 66), Bent,
Dickov (Guppy 77).
Subs Not Used: Nalis, Canero.
Booked: Scimeca, Dabizas, Thatcher.
Referee: M Halsey (Lancashire).