The Reds took the lead early on through Jamie Proctor, but King opened his account for the Bramall Lane outfit to lift them off the bottom of the table.
Proctor, who was rewarded with a start by Crawley manager Richie Barker after impressing off the bench in recent outings, put the visitors ahead inside 10 minutes.
Following a well-worked corner routine, the forward got on the end of Adam Drury's chipped ball across the six-yard box to head into United's net from close range.
Experienced centre-back Neil Collins came the closest to finding the Blades an equaliser in the first half when he glanced a header from a corner wide of the far post.
The hosts threatened again after the interval when Anthony McMahon struck the woodwork with a low 30-yard drive, and his effort rolled across the goal line before it was cleared by a Crawley defender.
United's pressure on the Town goal was rewarded just after the hour mark when King netted for the first time since being signed on loan from Birmingham City.
The Jamaican striker latched onto a through-ball from Febian Brandy before calmly tucking the ball into the bottom corner to prevent under-pressure manager David Weir going seven games without a point.