The linesman’s flag cut short Rooney’s celebrations in the sixth minute after he had got behind the Newcastle defence and finished past Tim Krul.
Mitrovic, on his first start for Newcastle, hit the crossbar later in the half before a late United onslaught saw Javier Hernandez denied by Krul before Chris Smalling hit the post in stoppage time.
After a week in which they failed to land Pedro, United lacked a cutting edge up front.
The result ended United’s perfect start to the season and provided yet more evidence that Van Gaal needs to add more attacking players to his squad before the transfer window shuts in 10 days’ time.
Rooney, who had scored 11 in 17 previous starts for United against Newcastle, looked to have ended his wait for a goal in the fourth minute when he latched on to Juan Mata’s through-ball and lifted the ball over Krul, but the goal was ruled out for offside
Despite his indifferent start to the season, Rooney’s confidence was high as he forced Krul into action from the edge of the area before the Magpies goalkeeper pulled off a smart save at his near post to deny Mata, whose free-kick he also comfortably kept out.
Steve McClaren, worried about his team’s poor start, came down to the touchline from the directors box.
The Newcastle boss had every reason to be worried. His team were creaking under pressure from United’s relentless attacking play. Mata and Rooney tested Krul again before Depay rounded his fellow Dutchman but was unable to finish.
As the first half progressed, Newcastle started coming back into the game.
Out of nowhere, Aleksandar Mitrovic leapt high to beat Matteo Darmian to the ball and rattle the bar.
Ayoze Perez then drilled a low shot wide after a mistake by Daley Blind.
United failed to take a grip of the game after the restart, with Depay wasting a good chance by firing a free-kick into the wall.
Van Gaal brought Michael Carrick and Hernandez on for Bastian Schweinsteiger and Januzaj as Rooney dropped into the number 10 position, leaving Hernandez up front.
The Stretford End yelled “Attack! Attack! Attack!” Van Gaal’s men obliged, but there was no breakthrough.
Steven Taylor blocked Rooney’s volley in the box and Mata blazed way over the bar after being found by his captain with a deep cross.
Luke Shaw played a neat one-two with Morgan Schneiderlin before driving a low shot at Krul, who then pulled off the save of the match to deny Hernandez from eight yards.
Fabricio Coloccini blocked Antonio Valencia’s shot, Chris Smalling struck the woodwork and a screamer from Carrick flew inches wide as United looked for another late goal at Old Trafford.
But it never came and Newcastle could have snatched all three points at the death had Papiss Cisse’s cross been converted by new signing Florian Thauvin on the counter.