Ryan Harding had to make a decisive tackle to deny Danny Invincibile after a Dean Keenan mistake but it was Ton who began to carve out chances.
Keenan had driven a fine drive just inches over and it was now Chris Templeman who took centre stage.
Graeme Smith had to sprawl to his left to divert a low shot from the tall striker then Templeman volleyed over a Jamie Stevenson cross from only seven yards.
Paul McGowan lobbed over from Chris Millar's pass before Steven Naismith hit a low shot under Paul Mathers only for Harding to clear near the line.
Naismith had a half-volley beaten away by Mathers and Templeman had yet another chance but, from Jim McAlister's cross he nodded wide at the far post.
It seemed that Ton would rue their missed chances just two minutes after the interval when Colin Nish stretched out a left foot to convert a Garry Hay cross.
At once, Jim McInally brought on Kevin Finlayson and the positive substitution paid dividends when Templeman hit a volley from Finlayson's cross past Smith from the edge of the box.
Six minutes later, Templeman controlled a Stevenson cross and turned sharply to fire a firm drive beyond Smith despite the keeper's hand reaching the ball.
Victory was complete when McGowan swept home a cut-back from McAlister near the penalty spot.