The Livi boss has cut a frustrated figure in away games since his side's promotion to the First Division but he finally got the monkey off his back thanks to goals from Mark McNulty and Mark Fotheringham.
And Bollan said: "It was about time we got a result away from home and it was thoroughly deserved in atrocious conditions.
"We had the advantage of the wind in the first half but Queens defended well and although we turned around one up, they came at us after the break.
"It took a fine penalty save from our keeper to keep us ahead before we got the second to make sure of the points."
Queens boss Gus MacPherson said: "After restricting them to one goal when they had the wind at their backs, the boys started the second period well.
"But the heads went down with the penalty miss."