Reds made it back-to-back away wins for the first time this season to make up more ground on their rivals at the bottom of the table.
The visitors fell behind to a Louis Dodds’ goal after three minutes but Anthony Wordsworth levelled with a deflected shot four minutes before the break.
Dodds restored Vale’s lead in first-half stoppage time – his sixth goal in as many games against Reds – but Crawley dominated the second half.
Izale McLeod equalised with a looping header (54 minutes) for his 17th goal of the season and Richard Wood powered home a 69th minute header for the winner, both goals coming from Wordsworth set-pieces.
Reds defended well in the closing stages to claim a deserved win which to within two points of safety.
Dean Saunders named the same side that won 3-2 at Colchester as Reds looked for their first win at Vale Park, scene of the club’s first Football League game back in 2011.
Reds made the worst possible start, conceding after just four minutes.
The visitors failed to deal with a corner from the right which dropped to the unmarked DODDS in the six-yard box and he had space to turn and lash the ball past a helpless Lewis Price.
Vale dominated early on, boosted by their early goal, and Colin Daniel wasn’t far away with a shot from the edge of the box on nine minutes.
Reds gradually began to work their way back into the contest without creating any clear-cut opportunities. Gavin Tomlin moved inside from his position on the right to try and give his side more control in midfield and gradually the visitors began to threaten.
Izale McLeod was desperately close on 41 minutes when Wordsworth’s pass found him on the right-hand side of the area and his volley was deflected wide for a corner, which the hosts cleared.
But three minutes later Crawley were level. Lee Fowler won possession in midfield and picked out Ryan Dickson’s run into the box on the left. He squared it to WORDSWORTH who fired past Chris Neal with the aid of a deflection.
On the balance of play it was no more than Reds deserved but deep into stoppage time they conceded a bad second goal when DODDS was able to pick his spot from close range after being found unmarked by Mark Marshall’s pass.
Reds regrouped at the break and after Mathias Pogba had failed to get his shot away from a good position they drew level on 54 minutes.
Wordsworth whipped in a great free kick which Wood headed on to McLEOD whose header from 12 yards looped over Neal and in underneath the bar.
Now the momentum was with the visitors and they deservedly went in front on 69 minutes. Wordsworth was again the creator with a corner from the right which WOOD met with a thumping header from eight yards that gave Neal no chance.
Just as they had at Colchester on Saturday, Reds had to withstand late pressure with substitute Ben Williamson heading wide in stoppage time as the home side won a barrage of corners.
But defend they did and back to back away wins have given Reds fresh impetus in the relegation battle as they prepare to entertain Leyton Orient on Saturday.