Jarvis was used on right side of midfield and when the chance fell for him after 37 minutes, he tucked it away.
His first attempt from a Neil MacKenzie corner was blocked but the rebound rifled past keeper Kenny Arthur.
He nearly doubled the lead on half-time but the introduction of Accrington’s Shaun Whalley at the break made it a different game.
Whalley sent shots flying narrowly wide and when he broke down the right after 76 minutes, Paul Mullin should have converted the cross.
County were hanging on and MacKenzie missed a great opportunity to clinch victory when he fired over. That set up a tense final 10 minutes and Ian Craney almost rescued a point for the visitors drove his shot wide.