The home side gave United an early scare when Paul Edwards's clever flick opened the goal up for Luke Rogers but Casper Ankergren was quickly off his line to block the striker's shot.
Despite being the League One's basement side, the Valiants continued to silence the 3,500 strong away following as they frustrated the visitors, pinning them inside their own half for long periods.
Seconds after having a penalty claims turned down, Manuel Rui Marques made sure his side went into the break ahead when he fired a right-footed volley past Joe Anyon after the Vale defence had failed to clear Bradley Johnson's corner.
Lee Sinnott's men were caught napping again two minutes later when Johnson turned provider once more to set up Dougie Freedman who finished comfortably into the goalkeeper's bottom left corner from 12 yards.
The game came alive once again when Andy Hughes was adjudged to have handled inside the area to concede a penalty.
After much protesting from Hughes and captain David Prutton, Vale's Paul Harsley stepped up to the spot in the 64th minute and confidently lashed the ball into Ankergen's top right corner.
Vale Park erupted again three minutes later when Rodgers' determination to win the ball enabled him to cross for Danny Whitaker who turned the ball into the back of the net.
Leeds refused to lie down and thought they had grabbed a winning goal four minutes before the final whistle when Tresor Kandol supplied a looping cross that Freedman placed expertly past the helpless Anyon.
But Vale bounced back once again in stoppage time when substitute Kyle Perry headed Harsley's free-kick across the face of goal where Rodgers was waiting to put the ball over the goal-line and level the scores for the final time.