Rangers were ahead after four minutes as Furlong collected the ball in the box and drilled home a low shot.
Then, with 15 minutes remaining, Pablo Counago brought down Lee Cook and Martin Rowlands' free-kick was thumped home by the head of defender Shittu.
Town, who have claimed just one point in their last three matches, can have no complaints after a mediocre display.
QPR boss Ian Holloway:
"I was delighted with the improvement they showed. It was a professional performance and I enjoyed it.
"I was expecting a backlash from Ipswich following their home defeat against Watford.
"We are still not safe. We need another win and when we get it I'll be taking them out to celebrate. To stay in this division on our budget is terrific."
Ipswich: Davis, Wilnis, De Vos, Naylor, Unsworth, Miller, Magilton (Counago 57), Horlock, Currie (Bowditch 72), Scowcroft (Westlake 57), Bent.
Subs Not Used: Price, Karbassiyoon.
Booked: De Vos, Scowcroft.
QPR: Royce, Bignot, Shittu, Rose (Miller 54), Edghill, Gallen, Rowlands, Santos, Bircham, Cook (Ainsworth 81), Furlong.
Subs Not Used: Cole, Padula, Cureton.
Goals: Furlong 4, Shittu 75.
Ref: A D'Urso (Essex).