A total of 81,978 fans turned out to see Spurs beat Jose Mourinho's men by virtue of Christian Eriksen's early strike and Phil Jones' own goal.
Spurs also held the previous Premier League record attendance, with 80,827 witnessing their thumping 4-1 win over Liverpool earlier this season.
Eriksen almost set a record of his own with his stunningly early goal, scored after 11 seconds, just two seconds slower than Ledley King's goal against Bradford.
It was, however, the fastest goal Manchester United have ever conceded in the Premier League.
Spurs are now just five points behind United, who remain second, and are two behind Liverpool and Chelsea in third and fourth respectively.
Manager Mauricio Pochettino was delighted with the performance and result, which kept Spurs firmly in the hunt for a top-four finish.
"It's a fantastic dressing room after a fantastic performance," Pochettino told BBC's Match of the Day. "The performance was great and I congratulate the players because they deserve all the credit.
"The first goal was a fantastic goal. Christian Eriksen believed that it would arrive in this situation. We tell the young players to always anticipate.
"I am so pleased we are in the race for the top four. There's a lot of games to play and that is why we need to stay focused.
"The early goal for us was good so that we can go on and dominate the game. That goal gave us more confidence and belief.
"It'll be tough against Liverpool now because they are one of the best teams - but it's about taking it one game at a time."