After failing to get the goal their control merited in the first half, United broke the deadlock in the 47th minute when Fred's 20-yard effort deflected in off Ben Davies. Bruno Fernandes then made the lead secure with just over 20 minutes remaining after curling a delightful first-time shot past Hugo Lloris from just inside the penalty area.
The win, achieved with Cristiano Ronaldo limited to the role of spectator from the bench, continued United's positive momentum under Erik ten Hag since a difficult start to the season. They stay in fifth place in the Premier League but are now just a point behind fourth-placed Chelsea.
"I am pleased with the team," Ten Hag said. "I think it was the best team performance this season.
"You have seen today we are developing. You see how we want to play, we get better on the pitch every time. Spurs are a magnificent team so far this season, I said to the lads in the dressing room it was enjoyable to watch you.
"It was a squad performance. What we have seen today, we have 11 players who defend and 11 who attack. I am pleased with that. I will not say that I am totally satisfied. That has to be the standard at Manchester United."
The one negative for United was Ronaldo leaving the bench and walking down the tunnel before the full-time whistle, something Ten Hag said he would "deal with" on Thursday.
The first half was almost entirely one-way traffic, with Lloris forced into a series of saves in the Tottenham goal to keep the game goalless.
It was Rashford, starting in place of Ronaldo, who had the clearest opportunity. And the forward might have done better after being played clean through by Fred but firing close enough to Lloris that it allowed the French stopper to get down and turn the ball behind.
The one time that Lloris was beaten in the opening half, Anthony, cutting inside on his left foot and curling toward the far corner, saw his effort clip the outside of the post.
But after all United's frustration in the opening half, it took less than two minutes into the second period for the hosts to finally make the breakthrough with a touch of fortune.
Fred's first-time shot from Jadon Sancho's pull back just outside the penalty box looked harmless until it clipped off the shin of Spurs defender Davies to leave Lloris flat-footed and find the back of the net.
Tottenham looked poised to grab an unlikely equalizer in the 68th minute when a cross found the previously quiet Harry Kane alone at the far post. But the England striker's shot was denied by David de Gea before the offside flag went up to render the action moot.
And just a minute later, Man United's lead was doubled. The impressive Fred was again involved, breaking into the box before Eric Dier got a foot in. The ball fell kindly for Fernandes, who gave Lloris no chance with a classy pinpoint finish.
United could have made the win even more emphatic but Rashford was again denied by Lloris when he perhaps should have scored.
Ten Hag's side had 28 shots in the match, the most by a team in a Premier League game this season. It was also the most a side managed by Antonio Conte has faced in a top-flight game, in the 318th league match he has taken charge of between Serie A and the Premier League.
"We have to be honest, United deserved to win," Conte said. "They started the game very well. In our side, we did not start the game. It was really difficult, because we made a lot of simple mistakes.
"The table is good, but every time we play a high level game, we struggle. I want to be honest -- against Chelsea we struggle, we lost against Arsenal and Manchester United we lost.
"In this type of game, I think that you need to arrive and not make big mistakes, with great concentration, great focus. You need to be ready to fight a war, or you die against your opponent. The level is very high, we are struggling."
Information from Reuters was used in this report.