Leading 3-1 with eight minutes to go City looked destined for an opening day league win, but were then clinging for a point after Wulfs fought back.
Craig Jones returned to the side after getting injured in the first pre-season fixture at Cheltenham Saracens back in July & there was also a return for Chris Withington who came on late in the game.
Both sides had chances early on but it was City who took the lead on 23 minutes. A long throw in from Luke English was met by Craig Jones who headed in from 10 yards out.
The visitors had a decent chance with two minutes remaining in the first half but City's new keeper Brendon Bunn saved well.
On 56 minutes City added a second after a well worked move. Dan Westwood was sent clear down the left wing by Chris Sterling & his pass was initially mis-controlled by Archie Muirhead but he then quickly regained composure before slotting home on his left foot.
City had further chances before the visitors pulled one back. City with a good opportunity to go forward, decided to go back & lost possession & from the resulting move Aaron Bishop headed home unmarked to make it 2-1.
Within a minute City stretched their lead in bizarre circumstances. A long throw in from Luke English was mis-handled by the Wulfs keeper and the ball dropped over his head into the empty net.
Two minutes later it was 3-2. After a cross in from the right wing, a goal mouth scramble saw the ball fall at the feet of the busy Jack Till who fired home from close range.
City saw another chance go begging before Wulfs pulled it level on 84 minutes. A free kick from the half way line played deep into City's box was met by a completely unmarked Jevons who had a simple header past the City keeper.
Wulfs nearly added a fourth in injury time but Aaron Roberts blocked well to deny the visitors a win.