City led 2-0 at the interval through goals from Ben Richards-Everton and Dylan Connolly while Argyle were reduced to 10 men after captain Gary Sawyer was shown a straight red card for a lunge on Connolly.
Bradford missed countless opportunities to go further ahead in the second half before Antoni Sarcevic was sent off after being shown a second yellow card.
But the visitors hit back with three minutes of normal time to play when substitute Ryan Hardie squeezed the ball through the legs of Richard O'Donnell.
After a nervy five minutes of stoppage time, McCall was relieved to hear the full-time whistle.
"There was relief when the referee blew his whistle because we have not managed the game like we should have done," said McCall.
"But against a good Plymouth side we are delighted to take the three points."
McCall hailed the work of the Bradford ground staff as the fixture went ahead despite poor weather conditions throughout the week threatening to postpone the game.
Referee Carl Boyeson carried out two pitch inspections before the game was given the go ahead just before 1pm.
McCall added: "The first shout out is the the ground staff and the volunteers who have got the game on.
"We said yesterday that we wanted the game on, we worked hard during the week without having the best training facilities.
"We got the call at 10.30am to say there was a doubt about the game going ahead. A lot of people worked a lot of hours to get that game on and we are delighted for them.
"And it is payback to them because we got the three points."
The result puts the Bantams to within two points of the play-off spots but McCall admits City could have made things easier for themselves with a third goal.
He added: "The pleasing thing is to see Dylan Connolly score, it was a fantastic finish.
"I am just as pleased with the first goal, we had plenty of corners against Newport and Grimsby and didn't really look a threat.
"If the delivery is right, we said we should be doing better with set plays and thankfully we saw that go in early on."