The Bantams were out of sorts against a well-drilled Exeter side in the first half and they looked like having a difficult afternoon when Matt Clarke's mis-hit clearance gave midfielder Matt Gill the chance to fire the visitors ahead after 38 minutes.
But a half-time pep talk from McCall fired up his side and, with wingers Joe Colbeck and Omar Daley terrorising the Grecians backline, Bradford turned the game on its head with two goals in five minutes.
Exeter keeper Paul Jones had made a couple of important blocks to frustrate the home side but, when he fumbled Colbeck's long-range strike after 53 minutes, hot-shot Thorne pounced on the rebound to stab home his seventh goal of the season.
The visitors had produced some neat football in the first half with striker Adam Stansfield causing all sorts of problems for Bradford's centre-half pairing, but the Grecians frontman will rue the chance he blasted against the bar in the opening period.
Thorne's equaliser was the spark that Bradford needed and, with the speedy Daley giving full-back Steve Tully a torrid time, more goals looked on the cards.
After 58 minutes the Bradford pressure told when full-back Paul Arnison swung over a perfect cross from the right and marksman Boulding rose at the back post to head home from seven yards.
As Bradford surged forward Exeter failed to stem the tide and, after another blistering run by Colbeck, Jones could only push away his shot and Thorne was on the spot to force the ball home from close range.
It was now one-way traffic and four minutes later Daley's sprint down the left flank sliced open the Exeter defence.
The Jamaican has been criticised in the past for wasting good openings but this time he kept his head to square the ball for Boulding, who drove a deflected shot beyond Jones from just inside the box.
Boulding almost grabbed his hat-trick after another mix-up in the box, but Jones stretched out a hand to flick his chip over the bar.
The visitors, who lost 6-0 the last time they came to Bradford in 1993, staged a late rally but Bantams keeper Rhys Evans was also on form and he superbly parried a Ryan Harley shot late on.