The Brazilian right-back's first half stunning goal put United on course to victory, which was sealed 10 minutes from time by Giggs.
Redknapp's QPR side are seven points away from safety with only 11 matches remaining, while United are edging closer to lifting their 20th title.
United's opening goal came in the 23rd minute with Rafael lashing a shot from 25-yards. Adel Taraabt lost possession in his own half, allowing Robin van Persie to hit a cross which Julio Cesar parried away but fell for Rafael, who smashed into the top corner.
Rafael came to United's rescue once again, but at the other end with a goal-line clearance to deny Christopher Samba's header. The Brazilian then sent a fine ball to Van Persie, who saw a left-footed volley saved by Cesar.
The Dutchman was later replaced by Danny Welbeck having picked a hip injury earlier in the half. Despite this injury United continued to dominate as they restricted Rangers to few chances.
Giggs, who turns 40 this year, scored 10 minutes from time to secure all three points. Nani put Giggs through and smashed past Cesar to give United a two-goal lead. The veteran later hit the bar while Samba, who was the only threat for United, brushed the post late on.