But the hosts were level on the half-hour mark, Daryll Meggatt heading home a Martin McBride corner.
Lawless came close when he hit the post in the 66th minute before Ian Watt slotted home Queen's Park winner four minutes into injury time.
Queen's Park: Strain, McGinn, Little, Millen, Meggatt, Anderson, McBride, Capuano (Sean Burns 82), Smith (Watt 72), Longworth, Daly. Subs Not Used: Hamilton, Gallagher, Quinn.
Goals: Meggatt 30, Watt 90.
Albion: Gaston, Reid, Benton, Donnelly, McGowan, Love, Stevenson, Canning, Chaplain (Ferry 79), Boyle (Gemmell 63), Lawless (Hamilton 76). Subs Not Used: Flynn, Lumsden.
Booked: Benton.
Goals: Lawless 15.
Att: 715
Ref: Thomas Robertson
Source: BBC Sport
Source: BBC Sport