Juan Mata's opener was canceled out by Jack Rodwell as the Red Devils again failed to register their first victory of the campaign.
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Despite starting slowly, Louis van Gaal's side took the lead as Antonio Valencia rolled in a perfect cross from the right, and Juan Mata was on hand to tap in a yard from goal.
That goal seemed to settle the Red Devils, but they were soon pegged back as Jack Rodwell powerfully headed home his first goal for the Black Cats since his summer move from Manchester City.
The visitors introduced Adnan Januzaj in the second half in search of a winning goal but weren't able to force Vito Mannone into a meaningful save after the break.
All eyes were again on Van Gaal after United began its campaign with a 2-1 home defeat to Swansea City last week. As if to add to the pressure, all three of the club's offseason signings – Luke Shaw, Ander Herrera and Marcos Rojo – were unavailable on Sunday.
Yet few would have predicted the level of disjointedness on display as United struggled badly, particularly in defense.
It was the home side which enjoyed the brighter start as United began nervously in possession, with Lee Cattermole - buoyed by a wonder goal against West Brom last week - hitting a half-volley just wide.
There were certainly signs of the nerves Van Gaal alluded to last week in his charges' display, although a botched attempt to play out from the back fortuitously led to an opening as Tom Cleverley curled over early.
But it was Sunderland causing most of the problems, the impressive Will Buckley cutting inside to feed Connor Wickham - who could only hit straight at David De Gea with the goal gaping.
Perhaps awoken by that miss, United responded to take the lead as Valencia found space on the wing and sent a vicious low cross to the back post that Mata was able to tap into an empty net.
But the goal did not bring an improvement in the visitor's general play and Sunderland leveled in the 30th minute, Rodwell heading home Sebastian Larsson's corner at the front post.
United did begin to see more of the ball after, although it was Sunderland which created the first half's final chance when Steven Fletcher's overhead kick went tamely wide.
Whatever Van Gaal said to his players at the interval did not have the desired effect as further poor defending let in Wickham, who saw his fizzing strike turned cleared off the line by Tyler Blackett.
Van Gaal's men then enjoyed a spell of pressure and were denied a penalty when Ashley Young went down under a challenge from former United defender Wes Brown.
The visiting side continued to press forward in search of a winner but, despite some nervous Sunderland defending, was not able to find the Midas touch in front of goal.