North End, boasting a 10-match unbeaten run going into the game, made the perfect start when defender Paul Huntington headed in a corner from Scott Laird after only nine minutes.
Josh Brownhill then doubled the advantage seven minutes later by latching on to a weighted throughball from skipper John Welsh and lofting the ball over goalkeeper Paul Jones.
Crawley, who introduced Andy Drury for James Hurst in a tactical change, awoke from their slumber in the 32nd minute when striker Billy Clarke headed wide from a deep cross from Nicky Adams.
Preston ended the half on top and 'keeper Jones gathered from the onrushing Stuart Beavon before Laird broke powerfully down the left and sent a fierce shot just over.
Veteran Crawley striker Alexander headed a Mat Sadler cross wide shortly after the break and Jones later dived to hold Brownhill's effort.
Town defender Walsh reduced the deficit for Crawley after 66 minutes with a low left-footed shot after a header by Mark Connelly had come back back off a post
Alexander had the ball in the net after 'keeper Declan Rudd failed to hold a shot by Emile Sinclair but the effort was ruled out for offside.
Walsh struck a post two minutes from time as the hosts pushed for a leveller, which duly came when Alexander forced home Adams' corner from close range.