The on-loan Bristol City striker fired home after a one-two with Bobby Grant.
Fleetwood goalkeeper Chris Maxwell saved Michael Bostwick's penalty after Shaquile Coulthirst was fouled by Eggert Jonsson, whose second-half header sealed victory.
Victory lifted Fleetwood into 19th, one point above the relegation zone.
Wes Burns scored his fifth goal in eight games as Fleetwood Town beat Peterborough to move closer to League One safety.