United, who lacked any fluency at the Stadium of Light, were fortunate to take a 17th-minute lead through Juan Mata.
However, they failed to take advantage as an unmarked Jack Rodwell headed in a first-half leveller on his home debut to earn Sunderland a point.
All eyes were again on the Dutchman after United began their 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 close-season 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 defence.
That they emerged with a point was perhaps a source of relief, with Connor Wickham spurning a great chance for Sunderland just after half-time.
It was the home side who 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 on.
But it was Sunderland causing all the problems, the impressive Will Buckley cutting inside to feed 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 Antonio 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 visitors' general play and Sunderland levelled in the 30th minute, Rodwell heading home Sebastian Larsson's corner at the front post.
United did begin to see more of the ball thereafter, although it was Sunderland who 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 visitors continued to press forward in search of a winner but, despite some nervous Sunderland defending, were not able to find the Midas touch in front of goal.
