The 21-year-old winger, on loan from Sheffield United, came off the bench to score with his first touch in the 73rd minute.
But Vale also had their own super sub in Ben Williamson, who struck two minutes later to level the scores.
The visitors failed to make the most a bright start, with Louis Dodds twice shooting into the arms of former Vale team-mate Stuart Tomlinson. Burton went on to fashion the better of the chances in a tight first half. Calvin Zola twice rose well to meet free-kicks taken by Lee Bell but could only direct his headers straight at Chris Neal.
With chances still at a premium after the break, Zola and Dodds missed the target for their respective teams. Neal also saved from Matt Paterson and Bell as the hosts continued to make most of the running.
The game came to life when Chapell's intended cross dropped into the far corner. But Vale hit back two minutes later when Williamson rammed home Jennison Myrie-Williams' low cross.