Gary Cahill's deep cross from the right found Graham Branch at the far post and his flick back across goal saw Akinbiyi nip in to score before half-time.
Branch was full of confidence down the Burnley left and made the most of hesitation in the QPR defence to jink in from the flank only to blast over.
QPR boss Ian Holloway on injuries to Shabazz Baidoo, Lewis Hamilton and Marc Bircham:
"It seems to be going that way for us. We have been falling over like skittles and that's one game we probably could have done with playing when it was scheduled for.
"I'm delighted with their efforts. Five of that team know their fates, they've signed for next year, four senior ones don't know their fate and some of the young lads who made their debut have been told they're not wanted by the club.
"We came here against an almost full-strength Burnley side and for large parts of the game we passed it quite well, moved it quite well and created one or two opportunities."
Burnley: Jensen, Duff, Cahill, McGreal, Camara, Grant (Oster 90), O'Connor, Hyde, Branch, Akinbiyi (Valois 90), Bowditch (Roche 89).
Subs Not Used: Coyne, Pilkington.
Booked: Bowditch.
Goals: Akinbiyi 43, 81.
QPR: Day, Bignot, Shittu, Edghill, Padula, Bircham (Mulholland 69), Cook, Baidoo (Hamilton 30), Kanyuka, Gallen, Cureton, Hamilton (Townsend 45).
Subs Not Used: Cole, Johnson.
Booked: Kanyuka.
Att: 10,396
Ref: C Oliver (Northumberland).