Cotterill had demanded that topsy-turvy Burnley should finish the season with a flourish and the much-travelled striker gave the Clarets fans a taste of things to come.
Cotterill believes that Burnley won't see the best of the former Stoke City frontman until next season, but the supporters were more than happy with Akinbiyi's contribution here.
Not that there was anything particularly special about his goals - a shot and a header from inside the six-yard box - but it was all about being in the right place at the right time.
Akinbiyi struck two minutes before half-time to give Burnley the lead when he pounced stylishly after a long ball from Gary Cahill had been headed back cross goal by Graham Branch.
Akinbiyi made the game safe midway through the second half when his quick reactions got him ahead of the visitors defence after great work down the left by the impressive Mo Camara.
Akinbiyi might have given Burnley an early lead but he was denied by a great block from Marcus Bignot.
Tony Grant tested Chris Day with a long-range shot as Burnely put Rangers on the back foot.
Rangers striker Kevin Gallen shot over when well positioned but Burnley were soon back on the attack and Dean Bowditch displayed great skill before hitting his shot on the turn too high.
Ian Holloway's side made a rousing start to the second half but they never properly recovered from an injury to one of their key performers, Marc Bircham, who was stretchered from the pitch with what looked to be a serious injury.
Burnley had the better of things late on and might well have added to their lead but Cotterill will be more than satisfied with a couple of goals from his new signing and the clean sheet.