The draw maintained the Blue Toon’s six-point advantage over the Fifers who remain five points adrift at the bottom of the cinch League 1 table.
But Jim McInally’s side have dropped a place to eighth, a point above Dumbarton who now occupy the relegation play-off spot.
In a match neither side could really afford to lose, Peterhead’s hopes weren’t helped by the difficult conditions and two enforced first-half substitutions.
Si Ferry went off with a back injury after 27 minutes, replaced by Hamish Ritchie, and eight minutes later Andy McCarthy limped off, to be replaced by Niah Payne.
Peterhead were inches away from the opening goal just before the second change as Grant Savoury beat keeper Jude Smith from 20 yards only to see the ball come back off the inside of the post.
The first period ended goalless but just three minutes after the restart the visitors took the lead as Kyle Connell rounded off a counter attack with a fine finish.
McInally made his final change on 63 minutes, replacing David Wilson with Ryan Duncan.
And the switch paid a quick dividend – just 11 minutes after coming on the on-loan Aberdeen teenager headed in a Payne cross to get his side back on level terms with his first senior goal.
McInally said afterwards: “It was a strange game, having to make early substitutions and the weather wasn't behaving itself.
"We then lost a terrible goal and were left to chase a game. We could have played better, we didn't get the ball out wide enough.
"But it's hard in conditions like that and when you're one down I would have seen the day we might have lost that game.
"But we kept at it and without playing particularly well. Our goalie's not had a save to make in the whole game, their goalie probably should have had more to make, but although we had a bit of pressure, we didn't really have enough clearcut chances."
Next up for Peterhead are away matches at Dumbarton on Saturday and at Montrose on Tuesday, December 22, a fixture brought forward from Boxing Day.