Tottenham did play plenty of attractive football - with Van der Vaart striking the woodwork - and more than matched United for long periods of the contest.
The home team have been wasteful at times this season, dropping six points from winning positions, including a 2-2 draw against West Brom after leading 2-0.
But after Nani's controversial goal was allowed to stand by referee Mark Clattenburg in the final minutes, United were able to close out the game with relative ease and remain third in the table, five points behind Chelsea.
United might have taken the lead inside two minutes when a crisp long-range strike from Ji-Sung Park smashed into the base of the post with Gomes well beaten.
Tottenham responded and Van der Vaart, who frequently dropped deep and found space in dangerous areas, crashed his thunderous left-foot strike against the United woodwork after eight minutes.
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Edwin van der Sar turned 40 on Friday but there was nothing wrong with his reflexes as he stopped a powerful strike from Luka Modric, while Van der Vaart missed with another effort from distance.
Robbie Keane made his second Premier League start of the season for Spurs as Peter Crouch dropped to the bench, and with Gareth Bale and Aaron Lennon out wide, the visiting team were extremely mobile across their front line.
However, for all their attractive attacking football, Tottenham often lacked a killer final ball, while United did occasionally prise open their opponents' defence.
Park shot wide after cutting inside, Rafael da Silva ended a surging run with a poor finish, and Gomes kept out a low strike from former Spurs striker Dimitar Berbatov, who has now gone six games without scoring.
But for all that there was to admire from both sides, the opening goal came via Vidic's thudding header after Spurs completely failed to pick up the defender as Nani swung in a free-kick from a wide area.
Bale had a relatively quiet match but did catch the eye with one electric run into the United area 10 minutes after the restart before shooting narrowly wide.
Spurs continued to create some promising positions but it was becoming increasingly evident that they were missing the extra option that a target man would provide, and Roman Pavlyuchenko replaced Keane after 61 minutes.
The substitute struck the side netting from 20 yards and Van der Sar denied Van der Vaart as the London side continued to press.
Javier Hernandez went close for United, while Nani thought he should have been awarded a penalty seconds before he scored his controversial goal.
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The Portugal international fell in the box and appealed for a spot-kick but, despite clearly handling the ball as he went down, he was not penalised by Clattenburg.
Gomes obviously thought differently and rolled the ball out as though his team had been given a free-kick, and he was punished when Nani slotted the ball home as the bewildered Spurs keeper looked on.
Arguments ensued, first between the United players and the assistant referee when it appeared he had ruled out the goal, and then between the Tottenham players and Clattenburg when the referee overruled his colleague.
Play eventually resumed, but with only six minutes remaining there was too little time for Tottenham to recover a two-goal deficit.
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