The former Swindon man signed for Exeter over the summer following his release by St Mirren and led the line superbly as the Grecians recorded a deserved 2-1 win.
Danny Coles set them on their way with a thumping header against his former employers in the 58th minute, but that goal was cancelled out 11 minutes later as Eliot Richards turned the ball home from Ellis Harrison's low cross.
But Parkin, who had been a constant thorn in the side of Rovers all afternoon, popped up with 11 minutes remaining to guide Arron Davies' cross into the bottom corner from 12 yards to the delight of boss Tisdale.
"Sam was outstanding on his debut. He really had a terrific game," Tisdale said. "Other than the goal, which is a major part of the game, his overall performance allowed us to get up the field and get into the opposition half.
"He offered a real challenge to the Rovers defenders and I don't want to ask too much of him too soon, but he showed that he is certainly capable of playing a game for us that is very, very important.
"I'm delighted. We made it a focus of ours that today was all about the result and a performance that led to a result.
"I think our game was basic at times and I will take any criticism of our play, which at times was forceful, but it had the desired effect and enabled us to be competitive throughout. And it was aided very well by Sam."
- Sports & Recreation
- Eliot Richards