Bobby Barr opened the scoring and shortly before half-time Andy Jackson sprang the offside trap to score the second. Robert Thomson added the clincher after 62 minutes.
In League Two, Peterhead stretched their advantage at the top with a 2-1 win at Stirling Albion.
Rory McAllister netted his 18th goal of the season midway through the first half after a defensive mistake to give Peterhead a deserved half-time lead.
Jordan White equalised nine minutes into the second half when he powered a header past Graeme Smith from a Craig Comrie corner.
But substitute Fraser McLaren scored what proved to be the winner midway through the second half with his first touch, an angled shot which beat Callum Reidford.
Annan Athletic kept up their pursuit with a 1-0 win over Montrose. Josh Todd scored the only goal from Alex Mitchell's cross early in the second half.
Berwick Rangers beat bottom club Queen's Park 1-0 with Darren Lavery scoring the goal 14 minutes from time.
And East Stirlingshire saw off Elgin City 3-0.