Colin Miles bundled into the diminutive striker who picked himself up to send Mark Goodlad the wrong way from the spot. But referee Ken Woolmer, who had earlier angered the home faithful by turning down penalty appeals and booking Nicky Maynard for diving, ordered a retake.
Rodgers, who has been out of favour at Crewe this season, kept his nerve to hit the second kick straight down the middle for a 93rd minute winner Dario Gradi's side just about deserved.
Home boss Dario Gradi must have been disappointed to see his team go in level at the break after his side's purple patch, which saw Gary Roberts strike the foot of the post, Maynard have a couple of efforts which went wide and Vale keeper Goodlad block Ben Rix's sweet low volley.
Apart from a Paul Harsley header which flew wide, Martin Foyle's men didn't look to be in contention.
When Roberts slid the ball into Maynard's feet the teenage striker got goal side of George Pilkington and took the ball past the advancing Goodlad for the Crewe opener in the 32nd minute.
But George Abbey worried rookie keeper Stuart Tomlinson with a rising drive with the outside of his boot which just missed the top corner.
And the Nigerian then demonstrated how dangerous he could be from long range when he belted a 30-yard shot into the bottom corner for Vale's 35th minute equaliser.
And Vale finished the first half the stronger and should have gone in front when Abbey's cross picked out Leon Constantine at the back post, but the big striker somehow headed tamely straight down into Tomlinson's hands.
Crewe seemed to suffer a real blow when Maynard was carried off with a hamstring injury midway through the second half, but they made light of it and came close to winning the game before the penalty with Rodney Jack and Rodgers having chances.