With the game poised at 1-1 after Marc McCulloch's equaliser, the keeper ensured they left with a point after two late, late saves.
John McGlashan took charge of Arbroath for the first time and his keeper was in action after just three minutes when he dived at Craig Smart's feet.
His struggling side almost stunned East Fife soon after when Pat Clarke set up Jay Stein with a neat back heel but his shot was blocked.
Steve Fortune then slid in to prevent Hugh Davidson after 14 minutes and John Dodds was lucky to escape when he dropped Davidson's cross moments later.
The Fifers were dealt a blow when Smart limped off but were ahead after 23 minutes when John Martin sprung the offside trap and ran through to coolly shoot past Peat.
Davidson almost brought Abroath level in the next breath but his fierce half-volley climbed just over the bar.
McGlashan's half-time talk certainly did the trick as Arbraoth equalised thirty seconds into the second period.
Alan Brazil's cross was perfectly lofted and McCulloch rose to glance the ball into the net.
Both sides pushed for the winner with Arbroath substitute Roddy Black testing Dodds with a low drive and Gary Kelly trying to catch out Peat with a chip.
The Arbroath keeper then earned his team a point with two tremendous saves.
In the 70th minute he ran from his goal and got an outstretched arm to Martin's goalbound shot and in the very last seconds he somehow blocked Sean Paliczka's low drive from just three yards out.