But the Reds were the architects of their own misfortune early on. Joel Lynch was sent off on 12 minutes after he elbowed Vale's Nathan Smith off the ball from a Crawley corner.
The Reds were under the cosh but defended excellently, and unexpectedly took the lead on 43 minutes thanks to Kwesi Appiah's fourth goal in five games.
But Vale responded magnificently in the second half. Tom Conlon, Tom Pett, a George Francomb own goal, and a late Port Vale strike consigned Crawley to their fourth consecutive league defeat - the first time that has happened under manager John Yems' tenure.
The Valiants had the best of the opening 10 minutes. James Wilson forced Glenn Morris into making two saves before Lynch's red.
After the sending off, naturally, it was all Vale. The visitors had a lot of possession, playing a slick passing game, but in truth failed to assert their numerical advantage.
Morris produced an acrobatic save to keep out Dennis Politic and did well to collect Conlon's 20-yard shot.
The Valiants' most clear cut opportunity came five minutes before the breal. Ben Garrity's header from a Conlon corner whistled just over the bar.
Crawley, to their credit, defended manfully. The Reds got players behind the ball and stuck to their shape, leaving Vale very few avenues to exploit.
And the host's resilience and perseverance was rewarded on the stroke of half-time. Appiah headed home from close-range after a delicious Tsaroulla cross to give the Reds an unlikely lead.
Crawley's opener lit a fire under Vale. Dan Jones unleashed a long-range rocket that Morris could only tip round the post, but Crawley held firm until the break.
The Reds' resistance was broken just two minutes after the restart. Conlon sent a free kick from the edge of the box up and over the wall and into the net for Vale's equaliser.
The Valiants then had a free kick in a similar position moments later, but this time Morris palmed the ball away.
There were shouts for a penalty from the home fans after Tyler Frost struck the ball at Mel Benning's arm from close range, but the referee was unmoved.
Pett then made a brilliant last ditch tackle to stop buccaneering substitute Mark Marshall from getting a shot away.
Vale ramped up the pressure. Jake Taylor headed agonisingly wide from a George Lloyd cross before Morris pushed away Jones' excellent curling effort.
And the pressure finally told with 15 minutes to go. Amoo collected the ball and laid it off to Pett who dispatched a right footed shot into the bottom corner.
Morris made a spectacular stop to keep Lloyd off the scoresheet before the Valiant made it 3-1 with 10 to go.
Amoo burst into the area and sent a dangerous ball towards the penalty spot but the unfortunate Francomb sent the ball into his own net.
And Vale added a fourth at the death. Conlon played a fantastic through ball to Amoo who went round Morris and slotted it into the Crawley net.
Crawley Town: Morris, Francomb (Payne 83), Lynch, Craig, Tsaroulla, Hessenthaler, Ferry (Davies 78), Powell, Frost (Marshall 65), Appiah, Nichols. Unused: Noukeu, Ashford, Rodari.