The Devils fell six points behind after the first two heats but they battled back to take six-point lead of their own by heat 10. The match remained in the balance at 36-all with three heats remaining.
Ryan Fisher, who top scored with 12 points from five rides, and skipper Kyle Newman turned the match in Plymouth ’s favour with a 5-1 against Lasse Bjerre and Andre Compton in heat 13 and the Devils were defending that lead in the final heat.
There was a dramatic finish, however, with Newman excluded from the last race for bringing down Bjerre.
However, Fisher did enough in the re-run to split Jason Garrity and Bjerre and ensure that Plymouth secured their narrow victory.
Co-promoter Ashley Taylor said: “It was a bit of a shock for us being 9-3 down after two heats, but we got to grips and managed to turn things around.
“It was a classic 15 heats of speedway with both teams happy after a nail biting finish. We had the win, and Sheffield went away with a consolation point from a narrow away defeat.
“The pleasing feature for us was that the Plymouth side rode as a team and showed grit and determination throughout the evening.”
Plymouth: Kyle Newman 8+2 (5 rides), Sam Simota 8+1 (4), Morten Risager 7+1 (4), Jack Holder 6+1 (4), Ryan Fisher 12 (5). Reserves: Ashley Morris 5+1 (5), Richard Andrews 0 (3).
Sheffield: Lasse Bjerre 9+2 (5), rider replacement for Ty Proctor, Ashley Birks 9+1 (5), Jason Garrity 12+1 (6), Andre Compton 6+1 (5). Reserves: Josh Bates 4 (5), Arthur Sissis 4+1 (4).