Hall watched his side take a Christmas stuffing from the hungry Fifers in a tale of two keepers.
Both number ones were excellent and James Butter showed his worth after seven minutes when he blocked Greig McDonald's drive.
Martin Wood looked lively for Hall's men and his low shot proved awkward for Scott Morrison, but he got gloves on the ball.
Morrison then raced from his line to deny Wood while Butter performed more heroics when his foot and defender Paul Doyle kept out Steven Nicholas' shot.
Montrose carried little attacking threat although Steven Kerrigan almost netted after 40 minutes but his header was well held.
Both keepers continued their scrooge act by giving nothing away and Butter made another crucial stop after 47 minutes from Jonathan Mitchell.
Neil Stephen's head was in his hands in the 55th minute when he somehow headed wide before Montrose missed the chance of the match.
Craig Smart sprung the offside trap but Morrison blocked Wood's effort and threw himself in front of Kerr Dodds' follow up.
Butter deserved better but was finally beaten after 69 minutes when Fairbairn cut in from the left and crashed a drive into the bottom corner.