It was the first win under his charge since taking over in mid-November and ended a run of 16 games without a victory.
McCall said: "I thought overall we were the better side and deserved to win.
"Airdrie did have the bulk of play in the second half, but our defenders didn't allow them to create any clear-cut chances."
Queens took just nine minutes to break the deadlock when Graham Weir was brought down by Stephen Robertson and John O'Neill gave the keeper no chance from the spot.
Airdrie were unlucky not to equalise just before the interval when Brian McPhee created an opening only to see keeper Colin Scott block his first attempt from six yards and then see his follow-up cleared off the line by Stuart Lovell.
It was all Airdrie after the break and it became almost a siege on the home goal with Queens toiling and their forwards only seen in rare breakaway raids.
But it was in one of those breakaways that they sealed victory in the 75th minute when Andy Thomson smashed in a shot which keeper Robertson could only palm away and Paul Burns was on the spot to net.
Aidrie manager Sandy Stewart was disappointed that his side's pressure had not paid off. "Whenever the ball did land in the Queens area it seemed to fall to one of their players, and we just could not get a clear opening," he said.
Duke's verdict - it wasn't pretty and Queens rode their luck at times but who the hell cares as the players gave 100% for McCall and we deserved the three points. Airdrie enjoyed a lot of the ball but Queens created far more chances and the game could have been over by half-time if Weir and Paton had not missed fairly easy chances.
Duke's Man of the Match - Another immaculate performance from Andy Thomson but this time it goes to Graham Weir who stuck to his task despite some crude tackling by the Airdrie defence.