United were looking to go above the Toffees in the table but Wayne Rooney and Danny Welbeck were both out of luck in front of goal when denied by the woodwork, and the Merseysiders took full advantage late on.
The Reds came closest to scoring in an evenly-matched first half when Rooney struck a post. The in-form hitman, playing against his first club, saw his shot deflect off both Phil Jagielka and Sylvain Distin before hitting the upright and Tim Howard diverted the rebound away from Shinji Kagawa.
There were a number of other close calls, with Kagawa losing out in a one-on-one duel with Howard while the keeper also denied Rooney, who was later booked and now misses the Newcastle game. Jagielka escaped with a handball inside the box and Kagawa's cross went through Rooney's legs in the middle.
The visitors also looked a threat, with Romelu Lukaku a powerful presence in attack as both he and fellow Belgian Kevin Mirallas brought David De Gea into action. After the break, substitute Gerard Deulofeu raced away with his first involvement but could not squeeze the ball through De Gea's legs while the champions should have broken through on 72 minutes. Howard pushed away Evra's header from a Rooney corner and Welbeck, having to readjust, could only head against the bar with the goal gaping.
Although De Gea appeared to touch a Mirallas free-kick onto a post, the ball was recycled and Lukaku scuffed the ball across goal where Oviedo was on hand to fire into the net and strike a killer blow.