The Devils were always in control after taking an eight-point lead in the first four heats.
Although the Panthers cut the deficit to two points after heat 10, Plymouth held on for a welcome away success with Jack Holder dropping only two points from his five rides.
The three away points still see the Devils in the bottom three of the table, but they are now only six points adrift of a top six place needed to achieve their target of reaching the end of season play-offs.
Peterborough: Brady Kurtz 9 (5 rides), Lewis Blackbird 5 (4), Robert Lambert 6 (4), Michael Palm Toft 13+1 (5), Ulrich Ostergaard 5 (4). Reserves: Rafal Konopka 0 (3), Simon Lambert 5+1 (5).
Plymouth: Kyle Newman 8+2 (5), Jack Holder 11+2 (5), Ryan Fisher 5+2 (4), Todd Kurtz 6 (3), Morten Risager 9 (4). Reserves: Matt Williamson 1+1 (3), Sam Simota 7+2 (6).