It had looked like Annan might concede ground at the summit, but McColm made use of a clever pass from Greig McDonald to ensure that his side were able to clinch three points at the death.
Fife conceded the lead on three separate occasions throughout the game, but they were finally able to seal a slender win thanks partly to a brace from Nathan Austin, who built on goals from Patrick Slattery, Jamie Insall and Kyle Wilkie.
Fellow promotion hopefuls Clyde also took three points from their home clash with Elgin City, where they still managed to score in abundance despite a sending off as they rose victorious with a 4-2 win at Broadwood Stadium.
Stirling produced an important win further down the league too, where they had second-half goals from Willie Robertson, Ross Smith and Steven Doris to thank as the home side were able to beat Arbroath 3-1.
Results in full: Annan 1-0 Berwick, Clyde 4-2 Elgin City, East Fife 5-3 East Stirling, Stirling 3-1 Arbroath