Juan Mata put United ahead in the 17th minute, providing a close-range finish to Antonio Valencia's cross.
But Rodwell broke his Black Cats duck 13 minutes later by heading in a Sebastian Larsson corner to draw things level.
The result means the Red Devils have got their first point of the new Barclays Premier League season on the board.
But just over a week on from their campaign-opening home defeat to Swansea, Van Gaal's men again looked unconvincing, even with Robin van Persie back in the team.
Earlier, Mauricio Pochettino's maiden home match as Tottenham boss saw his side thrash fellow London side QPR 4-0 and move to the top of the table.
The hosts were three up by half time after Nacer Chadli scored twice, either side of an effort from Eric Dier, adding to his winner at West Ham last week.
Emmanuel Adebayor netted after the break to wrap up a third victory from three games in all competitions for Pochettino this season and cap a thoroughly miserable return to White Hart Lane for QPR's ex-Spurs manager Harry Redknapp, whose team are yet to register a goal or point.
In Sunday's other top-flight encounter, Stoke controversially salvaged their first point of the campaign against 10-man Hull at the KC Stadium through a late goal from Ryan Shawcross.
After James Chester was sent off with just 14 minutes on the clock, Nikica Jelavic's finish just before the interval had looked set to steer Hull to a second successive league victory.
But the visitors made it 1-1 in the 83rd minute when Phil Bardsley's angled shot ricocheted off the inside of the post, against goalkeeper Allan McGregor and was nudged over the line by the waiting Shawcross.
Hull were left to fume, with the goal coming from a Stoke throw-in which should have gone the home side's way.