Michael Bostwick took the home side 2-0 up early on, before the Shaymen struck twice in 11 second-half minutes to snatch a point.
Bostwick gave Crawley the perfect start with a goal after just seven minutes. The 17-year-old, on work experience from Millwall, guided a header to the bottom corner from Danny Brown's inswinging free-kick.
Bostwick, making only his third League start, netted his second on 15 minutes. Striker Steve Burton drilled a low cross from the right flank and the young midfielder arrived late to slam home a side-footed effort from eight yards.
Halifax piled on the pressure after the break and halved the deficit on 57 minutes.
Tyrone Thompson threaded a ball into the path of half-time substitute Chris Senior and, as Crawley appealed for offside, the lively frontman slotted under on-rushing keeper Phil Smith.
Senior then turned provider on 68 minutes as the Shaymen completed their comeback. His cross from the right wing eluded the home defence and Lewis Killeen slid at the back post to tap into an empty net from close range.