Bradford City 0 Exeter City 1
The Bantams were beaten at home for the first time since Micky Adams' Port Vale came and grabbed all three points, but Parkinson's men have a chance to instantly put things right as they face Plymouth Argyle at home only 3 days after slipping up to Paul Tisdale's Devon outfit.
With the clock ticking down Garry Thompson wasted a glorious opportunity to equalise; with City going forward in numbers, McHugh headed the ball across the area and Thompson stabbed the ball wide with only Krysiak to beat.
Nahki Wells played a return pass to Carl McHugh to allow him to cross and his low delivery was almost bundled home for an own goal by Danny Coles as he got his legs in a tangle, but the ball was eventually scrambled clear.
A minute later City almost shot themselves in the foot when Rory McArdle's back pass lacked the pace it needed and Duke had to race out to clear the ball away with a slide tackle as Cureton had looked to nip in.
Substitute Alan Connell came closest to equalising when Wells teed him up to curl a first time shot from 20 yards that dropped marginally over the bar.
The Bantams began the second half on the front foot and Wells almost scored a fluke goal when his mis-hit cross had Krysiak struggling as he had to alertly push the ball over the bar.
Exeter always looked a threat going forward and they took the lead a couple of minutes before the interval; Craig Woodman got forward well from full back to deliver a deep cross that was nodded back by Matt Oakley and acrobatically tucked away by Jamie Cureton.
The stadium erupted into mass appeals when Artur Krysiak seemingly leant over the edge of the area to retrieve a loose ball; over 10,000 City fans thought it was a certainty he had handled outside the area but the ref thought otherwise.
After a contentious Exeter corner was half cleared, Pat Baldwin headed the ball back into the mix and it fell to Scot Bennett who blazed over from only a few yards out.
From one top scorer to the next, Nahki Wells was the next trying his luck. Duke's long punt forward was flicked on by Hanson and Wells hit a snapshot towards goal that Krysiak had to scramble behind for a corner kick.
Gow's movement was proving difficult to deal with and he found space to charge forward before threading a neat ball through to Cureton; with time and space in the area, the former Norwich City man curled a shot past Duke that cannoned back off the far post.
City then almost grabbed the opening goal with a header. Gary Jones' freekick was met by the head of James Hanson who thumped an attempt narrowly wide with Artur Krysiak struggling to get there.
Four minutes into the game, Exeter skipper Danny Coles had the first half chance; Alan Gow's floated corner was glanced across goal by the centre back with the ball edging narrowly wide.
In a game where The Bantams huffed and puffed but couldn't find the net, a solitary strike from The Grecians' leading scorer Jamie Cureton was enough to hand the Devon club all three points as City lacked the cutting edge they usually possess when playing at home.