The hosts went into the match with a new caretaker boss in Ryan Mason following Cristian Stellini's sacking after the humiliating 6-1 defeat at Newcastle.
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Spurs fans showed their anger towards chairman Daniel Levy and owners ENIC throughout the game, and even before the match with a protest outside the stadium.
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And they loudly booed their team off at both half-time as the Red Devils threatened to run riot.
But while they failed to fire five in past Spurs in the first half which Newcastle did last Sunday, United scored just twice through Jadon Sancho and Marcus Rashford.
In what was truly a game of two halves, Tottenham looked like a completely different team after the break.
Pedro Porro pulled one back in the 56th minute with an emphatic half-volley into the top corner.
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United then thought they had restored their two-goal lead after Bruno Fernandes smacked a shot off the bar, with Fraser Forster then denying Aaron Wan-Bissaka from the rebound.
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It was a miss that the visitors would rue as Heung-min Son tapped home from close range in the 79th minute after being picked out by Harry Kane.
Kane was serenaded by United fans in the first half with the travelling supporters dreaming over a potential summer transfer.
Spurs had the chances to win the game, as Son fired a strike well wide before his equaliser, while Eric Dier somehow missed his header from a few yards out.
The result leaves Spurs trailing United by six points in the table, and keeps their faint chances of finishing in the top four alive.
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Reacting on commentary for talkSPORT, ex-Chelsea defender Scott Minto said: "It was a fantastic game. Man United were superb in the first half and the scoreline flattered Spurs.
"But they stepped it up. The intensity was there. Whatever Ryan Mason said worked."