Spurs, who have won six of their last seven league matches, led 2-0 at halftime with goals from Bale and Van der Vaart, who scored for the fifth league game in a row to equal a club record shared by Teddy Sheringham and Robbie Keane in the Premier League era.
QPR, totally outclassed in the first half, came back strongly after the break and cut the arrears when Jay Bothroyd headed in from close range after 62 minutes, but Bale made the game safe with a stunning strike from the edge of the box after 72 minutes.
The win moved Spurs up to fifth spot on 19 points from nine matches, level with third-placed Chelsea and Newcastle United, who will move above Chelsea if they maintain their unbeaten League record at Stoke City on Monday (2000 GMT).
Manchester City, who beat Wolverhampton Wanderers 3-1 on Saturday, lead the standings with 28 points, five clear of Manchester United, 1-0 winners at Everton. The defeat left promoted QPR in 12th place with 12 points