Erik ten Hag’s side are battling to secure a seventh place finish in the Premier League, which could secure a place in next season’s UEFA Conference League.
United will qualify for the Europa League if they win the FA Cup final against Manchester City on May 25.
But if City triumph at Wembley then seventh will be enough for a Conference League spot.
And eighth-placed United are still in the hunt for that place after beating Newcastle to move level on points with the seventh-placed Magpies.
Goals from Kobbie Mainoo, Diallo and Rasmus Hojlund at Old Trafford gave United only their third win in nine league games.
However, United’s goal difference is vastly inferior to Newcastle’s, meaning they must better the Magpies’ result in the last game of the season.
United travel to Brighton on Sunday, while Newcastle head to Brentford.
Newcastle’s defeat means fifth-placed Tottenham are guaranteed to be in the Europa League next season.
Sixth placed Chelsea won 2-1 at Brighton in Wednesday’s other game to move closer to European qualification after a turbulent campaign.
United embarked on a sheepish ‘lap of honour’ after their final home game of the season.
And, while it has hardly been a campaign to celebrate, this was a much-needed result as Ten Hag fights to avoid the sack at the end of a season that ranks as one of United’s worst in the Premier League era.
“It’s important to win the last game at Old Trafford this season. The fans deserve this because they’ve had difficult times and always stayed with us,” Ten Hag said.
“We wanted to pay the fans back. We have Brighton in the last game which is important in the ranking. We don’t have it in our hands but we have to do our job.”