The veteran forward was recalled after Tuesday night's midweek draw with Crewe to fire the Pilgrims to their first home win of the season at the fifth attempt.
Evans struck when Burnley's defence failed to clear Rufus Brevett's cross from the left. The ball fell to him on his left foot, giving him just enough time to send a measured shot past Welsh goalkeeper Danny Coyne's outstretched right hand.
"I had this game in mind for Mickey," said coach Jocky Scott, who has taken charge of the Argyle first team while the Pilgrims board seeks a successor to Bobby Williamson.
"Sometimes I choose horses for courses and Mickey battered them last year and their manager was the first to admit it after the game. I told Mickey last Monday that he wouldn't be playing on Tuesday, that I was saving him for today.
"He scored the winning goal, which is great. He should have had more. If he'd scored with a header at the end, he would have spared everybody the grief of the last three or four minutes."
The first half was a largely cagey affair until around half-an-hour, when Burnley striker Ade Akinbiyi first forced Argyle's French goalkeeper Romain Larrieu into a good save, then cleared Mathias Doumbe's header from his own line.
Burnley came more into the game as an attacking force after Evans' early second-half strike, but the Pilgrims'defence, marshaled superbly by Nigerian international Taribo West stood firm.
Burnley nearly deprived the Pilgrims of all three points late in the game when substitute Graham Branch stooped to head James O'Connor's cross wide of Larrieu and, to Plymouth's immense relief, wide of the post.
Argyle, though, finished on a high, with match-winner Evans first forcing Coyne to tip a shot around the post and then flashing a header wide from substitute Tony Capaldi's subsequent corner.