The home side fell behind again on the hour mark when Scot Anson tapped home.
But Frank Carroll found the top corner to restore parity and Barry Douglas converted a penalty 15 minutes from the end to give the Spiders the win.
Queens Park: Peter Hamilton, Walker, Richard Sinclair, Little, Douglas, McBride, Capuano, Anthony Quinn, Chris Hamilton, Carroll (Daly 84), Holms (Murray 67). Subs Not Used: Black, McGinn, Dunlop.
Goals: McBride 48, Carroll 68, Douglas 75 pen.
Annan Athletic: Kelly, Muirhead, Neilson, Steven Sloan, Jack (Steele 69), Jardine, MacBeth, Cox, Anson (Storey 75), Bell, Watson. Subs Not Used: Summersgill, Inglis, Lewis Sloan.
Goals: MacBeth 40, Anson 60.
Ref: C Charleston
Source: BBC Sport