The hosts were inches away from taking the lead in the 19th minute when defender Chris Smith met Wes Fletcher's inviting cross only to see Luke McCormick somehow claw the ball away from finding the far corner.
Plymouth then threatened through top-scorer Lewis Alessandra as he collected Romuald Boco's ball in the area only to shoot wide of the target under pressure from Elliott Whitehouse.
The Minstermen wasted a double chance before the break with striker Ryan Bowman firing straight at McCormick before Whitehouse saw his effort smothered by the goalkeeper.
York's persistence finally paid off eight minutes after the restart with Bowman heading the opening goal after meeting Luke O'Neill's precise cross to find the far corner, the first goal Plymouth had conceded in almost 500 minutes.
Plymouth would soon restore parity 12 minutes later as substitute Tope Obadeyi made an instant impact as he headed in at the far post to take a point back to the south west.