KANE RICHARDS clinched the Blues a last gasp dramatic equaliser and a well deserved point.
Richards was introduced as a second half substitute and produced a headed equaliser two minutes into injury time from a Ryan Lloyd left wing cross.
Matt Fry had broken the deadlock for the Minstermen in the 70th minute with a header.
Chester made just one change to the side who lost 1-0 at Southport the week before in the FA Cup.
Midfielder Jordan Chapell replaced striker Kane Richards who was named as a substitute
York started on the front foot without seriously testing Blues keeper Liam Roberts.
Ryan Lloyd fired Chester's first effort over the bar from 18 yards after an incisive sixth minute pass from Craig Mahon.
But the Ministermen hit back a minute later when Johnny Hunt had to thump clear a n Alex Whittle cross and the resukling corner saw Roberts save an effort from Daniel Ntl.
Jack Higgins headed wide from a left sided free kick as York continued to press, but Mahon was unlucky to hit a first time piledriver from 25 yards which home keeper Kyle Letheren was well positioned to catch.
Durrell then kept the pressure on the home club with a 25 yard shot which deflected wide of the right post.
York had a great chance to score in the 31st minute when Scott Fenwick's shot hit Theo Vassell and rebounded to Simon Heslop before flashing wide of the right post.
Durrell saw his 30 yard free kick bounce wide of the left post in the 36th minute after he had been fouled by Heslop.
And Alabi held his head in his hands in the 38th minute after seeing his first time shot from the edge of the penalty area fly over the bar.
Chester looked a threat in the final third, but Lloyd failed to connect with a Mahon right wing cross, and Durrell's first time touch at full stretch friom an inch perfect Chapell delivery flew wide of the left post a minute before the break.
York started well after the interval, but Chapell forced Letheren into a good save after a well worked 51st minute manoeuvre.
Durrell came close to a breakthrough in the 60th minute when his 20 yard strike flew inches over the bar.
Alabi had a great chance to score in the 66th minute after racing clear but seeing his low shot saved by Letheren's feet.
But York went ahead in the 70th minute when Matt Fry headed home from a right wing corner despite the best attempts of Sam Hughes to clear off the line.
Chester worked hard to get back on level terms, but Durrell's 76th minute free kick hit the right post, and Richards hit the post with the goal at his mercy.
And substitute Richards produced a dramatic injury time headed equaliser from a left wing delivery by Lloyd. /
YORK CITY (4-5-1): Letheren, Whittle, Higgins, Fry, Oyebanjo; Rzonca (Klukowski 78), Kamdjo, Heslop, Clarke (Galbraith 64), Nti; Fenwick (Brodie 70). Subs not used): Flinders, Clappison.
CHESTER (4-4-2): Roberts; Hunt, Astles, Hughes, Vassell; Durrell, George, Lloyd, Chapell (Richards 66), Mahon; Alabi. Subs (not used): Lynch, Killock, Hudson, Joyce.
REFEREE: Simon Barrow.
ATTENDANCE: 2,639 (565 from Chester)
Full match report and pictures in Monday's Leader.
See full story in the Chester Leader