But, cruelly, Bob McHugh hit the equaliser for Queens fully five minutes into injury-time to give them a 1-1 draw.
It meant Alloa Athletic fans were celebrating their 3-1 defeat at Falkirk as they escaped the play-offs on goal difference. Mark Beck scored twice and Craig Sibbald was also on target for the home side with Alloa responding through Kevin Cawley.
Livingston beat Raith Rovers 2-0 in a meaningless tie at Almondvale. The Lions took the lead after eight minutes through Marc McNulty.
Craig Sives was sent off after 15 minutes for denying Greig Spence goalscoring opportunity. Joe Cardle struck a post as Raith sought an equaliser, but McNulty wrapped up victory for Livingston with a superb individual effort 10 minutes from time.