The visitors were the better side in the opening stages with a ferocious shot from man of the match Reed flattening Vale defender Clayton McDonald.
Alex Rodman was also inches away from converting a Reed cross, but it was Vale who took the lead against the run of play in the 29th minute. Ryan Burge slammed in his first goal in the Football League from eight yards after Michael Ingham's fine block from Tom Pope sparked a goal-mouth scramble.
Vale scored again two minutes before the interval when Chris Smith handled Chris Shuker's shot and Jennison Myrie-Williams slammed the resulting penalty low inside Ingham's right-hand post.
But York took charge again from the start of the second period and deservedly reduced the arrears in the 67th minute. The elusive Reed played a perfect pass into the path of Alex Rodman and he made no mistake with a low finish past the onrushing Chris Neal.
And Reed levelled the scores when he prodded home from point-blank range after Smith headed the ball into his path.