The 22-year-old joined St Mirren at the start of the campaign after a previous spell with fellow Scottish side St Johnstone last term.
He returned to United and played for 70 minutes in the outstanding 3-0 victory over Paris Saint-Germain in the Under-23s' Premier League International Cup group match last Friday.
Crawley must have been impressed, with head coach Gabriele Cioffi wrapping up a deal on deadline day for the League Two side.
There is a chance Willock could make his debut in the game at Bury on Saturday as he follows Ethan Hamilton (Rochdale) and Regan Poole (Newport County) in clinching loan moves during this window.