Queens boss Iain Scott rued that this was a game from which they should have taken all three points.
They completely dominated play throughout, although it almost cost them dearly in the final minutes when their defence was caught out by Brechin on the break.
The Dumfries men started strongly with David McNiven and Stephen Payne coming close. And then Tommy English was unlucky with a shot which just grazed the bar.
Brechin, however, almost caught Queens out with a break when Alex Burns was held back just outside the box and Gary Bollan's 25-yard kick went just over.
But it was Queens continuing to dominate, and they created a series of chances before the interval with Derek Lyle and Steve Bowey coming close.
Queens, however, were unlucky not to break that deadlock 20 minutes into the second half when Lyle managed to get in a shot from 25 yards and it was only a fine save by keeper Craig Nelson that prevented a goal.
Then in the dying minutes Queens keeper Richie Barnard had to bring off a double save from Alex Burns after the Brechin breakaway caught out the defenders.