North End were fortunate to find the net inside ten minutes as Chris Baguley’s fierce cross was flicked on and ricocheted off Josh Barrett leaving Hartley with no chance.
There was no element of doubt about the scorer of the second goal though as Baguley arrowed in from distance.
Taddy will feel aggrieved with the result after passing up on a number of good chances and limiting their opponents to only a handful of efforts.
Michael Morton made just a single change to the team that were unlucky to only draw at Droylsden last week as Laurence Hunter came in at left-back for his debut.
The Brewers, looking for their first win in the competition, almost got off to a perfect start inside thirty seconds as Corner set Aiden Savory away down the right-hand side and he was extremely close to picking out an unmarked Conor Sellars.
It was a fast start from Tad and there was only three minutes on the clock when joint top scorer Aiden Savory had his first chance.
A huge goal kick from Greg Hartley was misjudged by a North End defender and nodded backwards setting Savory in behind but he lashed off target.
Nevertheless it was the Hillmen who opened the scoring in the sixth minute, through a Taddy player however.
A corner found it’s way back out to Chris Baguley on the right wing and his devilishly dangerous delivery across the face of goal was flicked on and unfortunately turned in by Josh Barrett from close range.
In Barrett’s defence there was nothing he could have done about it as the flick-on bounced straight off his body and into the net.
Taddy almost responded immediately but were denied by the woodwork.
Josh Greening’s in-swinging free-kick was headed off the frame of the goal by Savory and Andy Milne couldn’t turn in the rebound.
Following the goal, the visitors seemed to click quickly into second gear as they had a decent fifteen minute spell of being in the ascendency.
With that being said, they weren’t carving Albion open.
The only half-decent chance for Glossop was when Conner Martin got the better of Barrett, drove up the by-line but his cross was hooked clear by Pete Davidson.
Speaking of Davidson, he had a chance of his own at the other end when a Greening corner dropped to the midfielder but he blasted high and wide.
There wasn’t a great deal of chances for either side in the first half but Taddy were furious with the officials with the break approaching when Aiden Savory was flagged for offside after a Tom Corner flick-on.
Half-Time: Taddy 0-1 Glossop
The Brewers started the second half like they did the first as Josh Greening’s deep right-footed cross was met by Tom Corner at the back post but the striker couldn’t generate enough power on the header to beat Russell Saunders.
Taddy were in charge as the game surpassed the hour mark as Saunders was tested again following a lovely passing move.
Hunter won the header, Sellars squared it across to Greening who picked out Aiden Savory and his powerful strike was well saved.
The home side were creating all the opportunities as just two minutes later they went close again.
Saunders punched a corner kick high into the air to which Tom Corner won and Andy Milne was pipped by a defender just at the vital moment of pulling the trigger.
With Greg Hartley untroubled, Taddy started to up the tempo with fifteen minutes to go.
Tom Corner and debutant Laurence Hunter both saw their efforts well blocked before Josh Greening performed several step-overs, cut inside and saw his effort held by Saunders once more.
But Glossop rode their luck, defended well when required and sealed the win eight minutes from time.
After a mini-game of head tennis, Chris Baguley got the ball down and rifled a low shot in off the post from 24 yards out.
Full-Time: Taddy 0-2 Glossop North End
Tadcaster: Hartley, Hardy, Hunter, Howarth, Milne (c), Barrett, Sellars (Murray 69), Davidson, Corner, Savory, Greening
Unused: Mycoe, Ellam, Dixon, Akeroyd
Glossop: Saunders, Haslam, Wood, Lacy, Jones, Meppen-Walter, Rick, Gee (Chippendale 53), Deegan (Oyibo 53), Martin (Hill 69), Baguley
Unused: Kisimba, Russell
Attendance: 227
Referee: Peter Henger