It took only seven minutes for Vale to take the lead as Jennison Myrie-Williams was given time and space down the left side before dispatching a low effort past Michael Ingham into the far corner.
Midway through the first half Vale missed a crucial chance to double their lead as Myrie-Williams saw his tame penalty easily saved by Ingham down to his left.
That miss seemed to lift the home side and Scott Kerr almost restored parity with a rare goal but Chris Neal clawed his effort away from the top corner.
Three minutes after the restart the visitors finally managed to get a second as Lee Hughes turned home an inch-perfect cross from the left by Myrie-Williams.
York pushed on as they looked to get back into the game but the closest they came was when Chris Smith headed high over the bar in the closing stages.