Spurs were awarded three penalties, two of which they converted, in their first home match in Europe's elite competition for 48 years.
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Manager Harry Redknapp's decision to play the tall Roman Pavlyuchenko and the even taller Peter Crouch paid dividends as the Premier League team overwhelmed their Dutch visitors.
"We picked an open team, we went for it... we knew there would be spells when they would hit us on the counter-attack but we went for it and got four goals, it was a fantastic result. It is about picking the right team and I picked the right team tonight," Redknapp told reporters.
Twente's coach Michel Preud'homme was upset about the penalties awarded against his side.
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"If you give a penalty on one side for stopping the ball with your hands, you have to give it on the other side also. Having said that, maybe Tottenham scored when they had chances, but we didn't," he said.
Redknapp's tactics brought three points and boosted their goal tally after they drew 2-2 with Werder Bremen in their Group A opener.
PENALTY MISS
The match began to turn Tottenham's way after 41 minutes even though Van der Vaart's penalty was palmed away by Twente goalkeeper Nikolay Mihaylov.
The Dutchman, recently signed from Real Madrid, almost redeemed himself with a stupendous volley which Mihaylov saved brilliantly, but a minute after halftime he made the breakthrough with a well taken goal from close range.
Pavlyuchenko put Spurs 2-0 up with their second penalty awarded when the flying Gareth Bale was brought down by Roberto Rosales, before Nacer Chadli pulled one back for Twente.
Van der Vaart was sent off just past the hour for a clumsy challenge on Rosales which earned him a second yellow card but Spurs weathered the storm and Pavlyuchenko made it 3-1 from the spot following a debatable handball by Wout Brama.
Spurs' fourth goal came five minutes from time when the outstanding Bale picked his spot after a typically surging run.
The victory left Tottenham level with European champions Inter Milan at the top of Group A with four points before their visit to the San Siro on Oct. 20 when they will be without the suspended Van der Vaart.
