United, fresh from their shock 2-1 defeat by Swansea at Old Trafford on the opening day last weekend, took a 17th-minute lead at the Stadium of Light when Juan Mata turned in Antonio Valencia's cross.
But former Manchester City midfielder Jack Rodwell equalised for Sunderland in the 30th minute when he headed in Seb Larsson's corner after evading marker Robin van Persie.
Gus Poyet's side caused a huge upset by winning 1-0 at Old Trafford in May as part of a 'great escape' that saw the north-east side avoid relegation.
But despite the urging of their Uruguayan manager, Sunderland couldn't manage a second goal, and nor could United, with van Gaal having said in midweek the team would need a "miracle" to win the league this season.
"The purpose of the game is to create more chances and score goals," Van Gaal told BBC Radio Five.
"We haven't created more chances, but in the second half we were more dominant than we were against Swansea. That's a plus, but we have to create more from that dominance.
Sunderland boss Poyet added: "A point is fair, I think so. We conceded a goal against the run of play a little bit.
"It's important we started better than last year (season) and that was key."
Earlier, Nacer Chadli scored twice as Tottenham Hotspur ensured there was no happy return to White Hart Lane for Harry Redknapp as they beat their former manager's Queens Park Rangers side 4-0.
Meanwhile 10-man Hull draw 1-1 at home to Stoke.
Chadli put Spurs ahead in the 12th minute when he thrashed home Emmanuel Adebayor's cross from six yards out.
Defender Eric Dier doubled Spurs' lead with his second goal in as many matches when he headed in Erik Lamela's corner at the near post on the half hour.
Tottenham went 3-0 up in the 37th minute.
Argentinian playmaker Lamela was again involved, his precise pass finding the head of Chadli, who nodded in from six yards.
- Disappointing -
Rangers did prevent Spurs adding to their tally until the 65th minute when Togo striker Adebayor side-footed home from six yards out after a fine run and cross by Danny Rose.
Victory meant Spurs went to the top of the table as one of only three sides, with Chelsea and Swansea, to have won both their opening games.
"I am happy to make two goals and help us to the win," said Chadli.
Championship play-off winners QPR -- who have Tottenham great and former England manager Glenn Hoddle working under Redknapp -- have now lost two out of two following their 1-0 loss at home to Hull on the opening weekend.
"It's a very disappointing day obviously. We started poorly and could have been one down in 30 seconds. We looked like a team of strangers," Redknapp said.
"Getting beat here is no different to anywhere else. It's just three points. That's all that matters to me."
Hull played most of the match a man down when last man James Chester was sent off in the 14th minute for bringing down Glenn Whelan on the edge of the box after being sold short by Jake Livermore's poor back-pass.
But Hull still took the lead three minutes before half-time when Nikica Jelavic scored form close range after Stoke 'keeper Asmir Begovic failed to hold a low shot from Tom Huddlestone.
It seemed the Tigers would hold out for all three points.
But Stoke equalised six minutes from time when, after Phil Bardsley hit the inside of the post, defender Ryan Shawcross did just enough to bundle the ball over the line, although Hull felt the throw-in that led to the goal should have gone their way.
"The throw-in was ours and blatantly ours," said Hull manager Steve Bruce.
Stoke boss Mark Hughes, who played in the same Manchester United side as Bruce, added: "The overriding emotion is frustration because we didn't play particularly well. We need to be better than that."
Saturday's matches saw Chelsea underline their title credentials in a 2-0 win at home to newly-promoted Leicester, while Arsenal showed impressive resilience in coming from 2-0 down to draw 2-2 at Everton.
Elsewhere, Swansea followed up their surprise victory at Old Trafford with a 1-0 win at home to newly-promoted Burnley.