Livi took the lead on 32 minutes when a cross from Shaun Byrne travelled to the back post where James Penrice flicked the ball home.
Right on half-time, Derek Lyle headed a James McFadden cross goalward for Queens but Neil Alexander leapt to his left to save and the striker was denied again by Alexander eight minutes after the restart.
The visitors thought they had grabbed a second on 62 minutes when Josh Mullin’s free-kick was met by Declan Gallagher but referee Colin Steven judged keeper Alan Martin pushed the ball away before it crossed the line.
A second did arrive on 68 minutes when another set-piece from Mullin flicked off the head of Dylan Mackin and into the net via the bar.
The hosts’ day got even worse when Kyle Jacobs was dismissed when he picked up his second booking, with Bryne lashing home a third with nine minutes left.