Owen Farrell booted 14 points and David Strettle dived over for the home side's only try to send Saracens top of a congested Pool One table.
McCall's men were deserved winners but had to hold their nerve after losing Will Fraser to the sin bin midway through the second half.
Munster failed to cash in on his absence as Ronan O'Gara's two late misses proved costly.
It means last season's beaten finalists are danger of failing to progress - they are three points adrift of the top in third - but Saracens now have their fate firmly in their own hands ahead of a tough trip to Racing Metro next month.
"Hopefully this was a bit of a coming of age for us but after four games you want to control your destiny," McCall said.
"We have to go to Racing Metro and potentially there are more twists and turns to come in this group.
"We played some really good stuff in attack and dug in when we needed to. Our performance had a bit of everything and we showed real character."
A 15-9 defeat to Munster at Thomand Park last weekend, when Farrell's radar was astray, had rendered today's match a virtual 'must-win' for Saracens.
With the pressure on, the home side's forwards stood tall and earned McCall's praise.
"We certainly improved from last week," he said.
"Our lineout had a 100 per cent success rate and we got on top in the scrum in the last 20 minutes."
Munster boss Rob Penney refused to concede his side's campaign was over with two games to play.
The Irish side travel to pointless Edinburgh next before a potentially decisive final-day encounter at home to Racing Metro.
"We have still 10 points to play for and who knows what will happen," Penney said.
"I am very optimistic that this group of players can turn this around as they are hugely talented."
Penney admitted Saracens had deserved their success after a vastly-improved performance from eight days ago.
The visitors' only try came via a Doug Howlett intercept on 26 minutes with O'Gara kicking eight points.
"I can't praise the boys highly enough, but their scrum improved substantially and their lineout was very good," he said.
"They kicked two penalties in our 22 at crucial times and it is as simple as that really."
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