Despite operating rider replacement for injured skipper Kyle Newman, the Devils took an eight-point lead in the first two heats and extended that to 19 points by heat nine.
It was not until the closing stages that Sheffield hit back with three 5-1 heat wins in the final four races.
Devils team manager Lee Trigger said: “I was very pleased with the efforts of the whole team. It was a good result to get a winning start to our home fixtures in the Premier League and three points on the board.”
Todd Kurtz took over as captain from Newman and top scored for the Devils with 14 (paid 15) points from his six rides.
Trigger added: “Todd led by example. He was buzzing in the pits and also did the work out on the track.”
Plymouth: Charlie Gjedde 5+1 (4 rides), rider replacement for Kyle Newman, Jack Holder 8+1 (5), Todd Kurtz 14+1 (6), Sam Simota 11 (6). Reserves: Stefan Nielsen 9+5 (5), Ellis Perks 5+1 (4).
Sheffield: Simon Stead 7 (4), Dimitri Berge 1 (3), Kyle Howarth 15+2 (5), Josh Bates 4 (4), Jason Garrity 7+2 (5). Reserves: Richard Hall 4+1 (5), Nathan Greaves 3 (4).