Spurs extended their unbeaten League run to seven matches with a superb first-half performance and a gritty rearguard action as QPR made a game of it after being outclassed in the opening 45 minutes.
Spurs led at the break through an angled drive from Bale after 20 minutes and an opportunistic effort from Van der Vaart, who scored for the fifth successive league match to equal a club record shared by Teddy Sheringham and Robbie Keane in the Premier League era.
QPR hit back when substitute Jay Bothroyd headed in his first goal for the club to make it 2-1 after 62 minutes and maintained the upper hand for a spell, before visibly wilting after Bale added his second goal
The Wales international produced a stunning strike from the edge of the box after 72 minutes following a brilliant exchange of passes with Aaron Lennon.
"I thought Spurs were fabulous and at half-time it would have been easy just to think how many they were going to get, so I decided to make changes and we came back strongly after showing them too much respect," QPR manager Neil Warnock told reporters.
"I even found myself clapping their third goal, it was just a such a fabulous goal," he added.
"They are a top team, full of class but we can take a lot of credit from that performance today, we have come a long way since Fulham [a 6-0 defeat a month ago], and we made them work very hard for it in the second half."
Tottenham manager Harry Redknapp said his side should have been 4-0 or 5-0 ahead at half-time.
"But then when you find yourselves only 2-1 up, it's difficult," he said. "But we finished it off with Gareth's goal to keep this great run going, I am delighted."
Warnock also praised his defender Anton Ferdinand, who has admitted enduring a stressful week after being the unwitting victim of an alleged racist slur from England captain John Terry during last weekend's match against Chelsea at Loftus Road.
The alleged insult was shown on YouTube and has prompted an investigation by the FA with the Metropolitan Police also showing an interest. Terry has denied the allegations.
"Anton showed great character today and did not put a foot wrong," said Warnock whose promoted team lie 12th in the standings. "I thought he was the man of the match. He is defending superbly and did very well today."
The win lifted Spurs up to fifth spot on 19 points from nine matches, level with third-placed Chelsea, who lost 5-3 at home to Arsenal on Saturday, and Newcastle United.
Manchester City, who beat Wolverhampton Wanderers 3-1 on Saturday, lead the way with 28 points, five clear of Manchester United, 1-0 winners at Everton.
Newcastle United will move above Chelsea if they maintain their unbeaten League record at Stoke City on Monday.
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