Despite dominating the game from virtually start to finish, McCall's men found themselves trailing until a late double from Charlie Wyke, including an injury time winner, claimed the points for the Bantams.
The memorable success - played out in front of a vocal home support - lifts City up to fourth in the Sky Bet League One table.
Speaking about the late drama, McCall said: "That is probably the most I've celebrated a goal in a long time.
"It was such a relief when the ball broke to Charlie (Wyke) and he put it in the back of the net (for his second goal).
"Although we went in at the break at 0-0, we've hit the post through Charlie and had some great chances, especially from set-pieces.
"The second period was a similar story really. We've made some more scoring opportunities and their 'keeper has made some good saves.
"As we've pushed though, it has maybe left us a little bit open, and they have scored a really good goal.
"Thanks to the absolutely tremendous backing we received, we've managed to get back into the game.
"I think the noise actually seemed to go up even more once they scored.
"It seemed to lift the players, and they have in turn shown their character and desire to win.
"On top of his goals, I thought Charlie's overall play was outstanding for us.
"He was unfortunate not to actually score in the first half with a towering header (that hit the post).
"Charlie will deservedly get the headlines, but I thought (Mark) Marshy deserves a lot of credit as well.
"He had an assist for both goals, and he also set up Charlie for his header that hit the post.
"It would have been injustice if we hadn't won today (Saturday) but it is all about coming off the park now with the three points regardless how you get them."