Elliott Durrell and Alefe Santos came in for the injured Brandon Smalley and Liam Cross in Mike Cook's only changes from Tuesday's 2-1 win against Peterborough Sports.
Jonny Ngandu’s strike on nine minutes was enough to secure all three points on the day, the win meant The Quakers leapfrogged City in the table.
Durrell returned to his favoured midfield position, as Cook opted for a 4-2-3-1 on the day, with Santos operating on the right flank from the start.
The Quakers went 1-0 inside the opening 10 minutes after Ngandu got on the end of a delightful reverse ball from Adriano Moke, which allowed the forward to cut inside and fire past Zach Jeacock into the top right corner.
Harry Emmett nearly equalised with a lovely flick on header towards the near post off of Jamie Reckord's inswinging delivery, but the midfielder's headed effort rolled just wide.
Ngandu came close to a second as the forward dribbled towards the edge of the box and tried his luck from the edge of his area but to no avail as his shot sailed wide of Jeacock's far post.
Reckord came desperately close with a lovely effort from 30 yards which forced a brilliant save out of Tommy Taylor in The Quakers net.
Durrell was an early second half casualty as Danny Wright came on in the 52nd minute as Cook switched to a flat 442 to search for an equaliser.
Wright came close to an equaliser but had his close range effort blocked by Toby Lees.
Ben Richards Everton was the next to test The Quakers' resolve as his looping header sailed just wide of the far post on 72 minutes.
Joe Parker had an effort after getting on the end of a ball supplied by substitute Wright, but the forward saw his effort blocked by Ben Hedley.
Quakers substitute Bradley Williams nearly doubled his side's lead with a strike that flashed across the face of Jeacock's goal, but the forward couldn't convert from a tight angle.
The defeat means City will see out the rest of the calendar year in the drop zone, Cook’s men will be back in action on Tuesday night at home to Curzon Ashton hoping to get back to winning ways.
The match report was detailed and quickly marked the end of their home winning streak. The result served as a reminder that, like in geometry dash scratch even a small setback can break momentum and overturn the challenges of a match.