The Saddlers, ahead through an early goal from Febian Brandy, were pegged back by Billy Clarke's strike before Ashley Hemming's restored their advantage 15 minutes from time.
Crawley finished with 10 men after defender Joe Walsh received a straight red card for a professional foul on Brandy six minutes from time.
Striker Forte, playing his final game before the expiry of his loan from Southampton, rescued Crawley a draw by heading in a cross from Nicky Adams in the 82nd minute.
Will Grigg headed wastefully wide at the near post for Walsall before Brandy fired the Saddlers ahead after 14 minutes with a low shot following a pass from Jamie Paterson, but Crawley levelled eight minutes later through Clarke, who rifled his seventh goal of the season after being set up by Forte.
Crawley had a let-off 11 minutes after the break when Paterson cut in and thundered a fierce right-footed shot against the crossbar, while midfielder Hemmings restored Walsall's lead with a close-range shot 15 minutes from time after Jones superbly parried a shot Sam Manton.