For Brechin it keeps alive their hopes of catching the Dumfries club with still six points separating the two sides.
Queens showed their intent from the start with only a tremendous one-handed save from Craig Nelson preventing Andy Thomson heading his side ahead after three minutes.
But Brechin came more into the game as Queens failed to cash in on early pressure, and they were unlucky after 23 minutes when Steven Hampshire found himself in the clear and beat keeper Colin Scott with an angular drive, but Jim Thomson was on the line to clear.
Scott pulled off fine saves when Hampshire again got through the defence, and then Chris Templeman saw the keeper stop a 20-yard drive.
At the other end it was only a tremendous double save by Nelson from Paul Burns and Graham Weir that prevented a goal, and from the resultant corner Ally Mitchell cleared the header from Weir off the line.
Manager McCall brought on youngster Michael Mullen in a bid to inject more life into the game, and the youngster duly obliged with a couple of runs which had the Brechin defenders struggling.
Nelson was again the hero when he stopped a shot from substitute Gary Wood at point-blank range. Then Craig Johnson cleared a shot from Derek Lyle off the line as Queens laid siege to the visitors' goal, but the Dumfries men just could not break through a rock- like Brechin defence.
DUKE'S VERDICT - Only an inspired display by the Brechin defence prevented Queens from scoring the proverbial barrowload. Having said that Thomson and Wood both missed easy chances to bury the Angus men. A disappointing scoreline but another solid performance from McCall's men and we are also one point nearer to the Cleyholers.
DUKE'S MAN OF THE MATCH - This time it goes to McStay who had his best game for Queens showing excellent control in midfield.