In a rather tentative fixture at Somerset Park, the hosts' vital goal arrived in the first half, where Alan Trouten's finish was enough to clinch three points as he made use of Nicky Devlin's assist after 38 minutes.
The victory was to prove vital given that Dunfermline Athletic were able to earn an important win over Airdrieonians, who succumbed to goals from Michael Moffat and Shaun Byrne as Allan Johnston's charges climbed into second place in the table.
Forfar Athletic suffered a frustrating afternoon away from home as they were held by a 10-man Stenhousemuir side, as finishes from Iain Campbell and Danny Denholm were cancelled out by Colin McMenamin and Jason Scotland late in the second half.
Down towards the bottom of the league, Cowdenbeath pushed themselves home to a 3-0 win over visitors Brechin City, where goals from Dean Brett, Ali El-Zubaidi and Greig Spence clinched three points for the hosts at Central Park.
Results in full: Airdrieonians 0-2 Dunfermline, Ayr United 1-0 Albion Rovers, Cowdenbeath 3-0 Brechin, Stenhousemuir 2-2 Forfar