Fullback Andy Goode also impressed for the home side, with the designated goal-kicker weighing in with 15 points through three conversions and three penalty goals to help overcome a determined Quins outfit.
Tigers found themselves quick out of the starting blocks, with a Goode penalty goal after just two minutes putting them ahead by 3-0, but 3-0 soon became 17-0 when Van der Westhuyzen and former All Black No.12 Daryl Gibson touched down, with Goode adding the extras.
Quins eventually got on the scoreboard through two Andy Dunne – a late starter after the injury-enforced withdrawal of Paul Burke – penalties, but Tigers went into half-time 17-6 up.
Fullback Gavin Duffy got his side's first try right after the break, with Dunne converting, putting the visitors in striking distance for the first time at 17-13 with almost an entire half remaining.
The home side just kept their noses in front, however, thanks to two Goode penalties, even though the visitors threatened briefly when Dunne kicked his third penalty and centre Josh Taumalolo scored an opportunistic try – leaving the score at 23-21.
But Van der Westhuyzen collected his double from the re-start and Goode again converted to give the home team another win in the post-Dean Richards era – a victory that keeps alive their chances of claiming a place in the Zurich Wildcard play-offs.
For Leicester Tigers:Tries: Van der Westhuyzen 2, GibsonCons: Goode 3Pens: Goode 3
For NEC Harlequins:Tries: Duffy, TaumaloloCon: DunnePens: Dunne 3