Two goals in two second-half minutes were enough for Spurs to take command of the match after a goalless first half where the hosts had edged proceedings.
Harry Kane headed home Kieran Trippier's corner on 50 minutes to put Spurs in the lead. Lucas Moura quickly doubled their advantage, as he curled Christian Eriksen's pass past goalkeeper David De Gea.
The Brazilian then wrapped up the game with six minutes of normal time remaining. He took a pass from Kane and raced past Smalling before finishing confidently past De Gea.
Mourinho's Lack of Ideas Exposed
Jose Mourinho caused a stir with his team selection, as he recalled Phil Jones and Chris Smalling in a back three alongside midfielder Ander Herrera. Eric Bailly was left out of the squad altogether, while Victor Lindelof was left on the bench.
BBC Sport's Simon Stone offered an explanation for the lineup:
Mourinho's team selection was a real gamble, and one that backfired in spectacular fashion. United were shaky defensively, with Herrera badly at fault for the second goal.
Former footballer Danny Higginbotham highlighted their problems in defence:
Mourinho also had few ideas of how to get United back into the game after they had gone 2-0 down. Alexis Sanchez arrived for Herrera but made little impact.
Marouane Fellaini was also predictably sent on as Mourinho sought a more direct approach. Adam Crafton at the Daily Mail was critical of his approach:
There's a growing sense of unease around Old Trafford with Mourinho failing to get the best out of a squad full of attacking talent such as Sanchez, Romelu Lukaku, Marcus Rashford, Juan Mata and Anthony Martial.
There's also an awareness that Mourinho is into his third season at Old Trafford and has a reputation for self-destructing at this point in his tenure:
Per Opta, this result was Mourinho's biggest home defeat as a manager in any competition. Two defeats out of their first three Premier League games has also highlighted a worrying lack of ideas from Mourinho.
Shaw Deserves England Spot Ahead of Rose
One of the few bright spots for Manchester United on Monday night was the performance of left-back Luke Shaw, who easily outshone his opposite number Danny Rose.
The 23-year-old has managed to force his way back into the team so far this season and has impressed in the opening games.
He was one of United's better players at Old Trafford in a performance full of energy, drive and a willingness to get forward and join the attack.
Football writer Andy Mitten shared his thoughts:
His performance also provided a stark contrast to Rose, who was making his first appearance of the new campaign for Spurs.
Rose flirted with disaster in the first half when a careless pass back to Hugo Lloris was intercepted by Romelu Lukaku. The Belgian ought to have opened the scoring but put his shot wide.
Football correspondent Kieran Canning said Shaw deserves a place in Gareth Southgate's England squad:
Shaw is showing the sort of form that persuaded Manchester United to invest heavily in him back in 2014. The challenge for the defender now will be to maintain his level and his place in the team under Mourinho.
Lucas Deserves His Spot
Lucas was Tottenham's best player on Monday night and fully deserved his two goals. He took both confidently and now has three for the season after also finding the back of the net against Fulham.
The Brazilian struggled to make an impact when he arrived in January from Paris Saint-Germain. However, he now looks settled and hungry to succeed in the Premier League.
Ligue 1's Matt Spiro feels he will thrive at Spurs:
Lucas has been given a real chance to stake a claim for a place in the starting lineup with Heung-Min Son away at the Asian Games. His pace, finishing ability and willingness to run at defences causes all sorts of problems and gives Spurs an extra attacking edge.
Son enjoyed a strong campaign last season and scored 12 Premier League goals. On this form, he will struggle to get back into the team ahead of Lucas.