Playing with a gusty wind at their backs in the first half made life difficult for the hosts in the early stages of this game, with some scrappy play on display for the opening 30 minutes.
Once Peebles got things under control, however, mainly thanks to the efforts of Sean Conaghan in midfield, the floodgates opened.
Daniel McAleavy capitalised on a mistake in the visiting defence to score the opener and, with momentum building, Frankie Arthur got another minutes later, when he broke through to expertly chip the Burntisland goal keeper.
Conaghan completed the first-half scoring with a great solo run to calmly slot the ball home.
With the wind in their faces after the restart, the message from Peebles manager John O’Hara was that three goals would not be good enough to win the game.
His team duly complied and further successful efforts from Scott Sutherland, McAleavy and club captain Dale Richardson, sealed a very convincing league win for the Whitestone Park men.
“I am delighted with how we played, especially preventing a well-organised Burntisland team from really getting going at all,” said O’Hara.