A goal from Jason Kerr, who was later sent off, saw Queens move into the top half of the table as basement boys Brechin were again left searching for their first win of the campaign.
Visiting boss Gary Naysmith said: “We faced a fair bit of pressure from Brechin towards the end of the match but the players defended really well to make sure we went away with all three points.
“That’s the first time in three years that we’ve had three successive clean sheets so I’m really pleased about that.”
The first half was evenly contested with both teams pushing forward in an effort to grab the opening goal and the Doonhamers came very close on the half-hour mark when City keeper Graeme Smith brought off a great save to tip a Lyndon Dykes volley over the bar.
City hit back and passed up a good opportunity five minutes later when a great pass from defence from Gary Fusco sent Isaac Layne racing clear but the striker prodded the ball past the post.
That miss was to prove costly for City as Queens made the vital breakthrough on the hour mark when the ball fell kindly for Kerr just inside the City box and the defender drilled the ball into the bottom corner of the net.
The game ended on a sour note just seconds from time when City’s Ally Love and goalscorer Kerr were sent off for an off-the-ball incident.
City boss Darren Dods said: “The players put so much into the game and we had the best chance of the match in the first half but I’ve no doubt we’ll clinch that first win if the players keep playing the way they’ve been doing.”