The former Swansea striker broke the deadlock by heading in a Nicky Adams cross at the far post after 77 minutes and then two minutes later he rifled in from 15 yards after being set up by substitute Josh Simpson.
Striker Paul Hayes, making his home debut on loan from Brentford, almost gave Crawley the lead after 14 minutes when his fierce left-foot shot came back off the underside of the bar after being teed up by Mark Connolly.
The hosts carried the greater threat throughout and Proctor had a goal-bound header saved from a corner by Mat Sadler before Crewe keeper Steve Phillips turned a shot from Proctor round the post.
Crewe threatened for the first time 10 minutes before the break when an accurate 20-yard drive from Ajay Leitch-Smith was well saved diving to his right by keeper Paul Jones.
Matt Sparrow put a deflected shot over for Crawley shortly after the break and Sadler was also off target inside the area when closed down by Mark Ellis.
Crewe produced few clear-cut opportunities in the second half and Leitch-Smith blazed their best chance wastefully over three minutes from time.