The Minstermen started the brighter of the sides, with Accrington goalkeeper Paul Rachubka forced into two saves within the first five minutes as he denied Adam Reed and Daniel Parslow.
York's positive start continued with Ashley Chambers wasting a golden chance to give them the lead - Rachubka denying the forward after bursting through on goal before Peter Murphy blocked Reed's effort on the line.
The hosts finally made the breakthrough in first-half injury time as Reed calmly slotted the ball home at the second time of asking after collecting Josh Carson's ball inside the area.
Just past the hour mark Michael Ingham was forced into his first meaningful save as he tipped James Beattie's deflected drive past a post with the ball creeping into the net.
Accrington came close to levelling in stoppage time as Michael Coulson blocked Beattie's effort before Murphy did rescue a point, bundling home Lee Molyneux's corner.