Defender Mat Sadler gave Crawley the lead after only 14 minutes with an angled left-footed free-kick, which sailed into the top corner.
Sadler was later well positioned to deflect a goal-bound shot from Michael O'Connor over his own crossbar.
The Millers pulled level nine minutes before the interval through Kieran Agard, who struck to head in from close range after a corner from Pringle was headed on by Kari Arnason.
Rotherham striker Alex Revell should have hit the target in first-half stoppage time when he wastefully put the ball over from Pringle's cross.
Morgan headed a Pringle corner wide and striker Lee Frecklington drove narrowly wide from 25 yards as Rotherham continued to get on top.
Substitute David Worrall settled the issue 13 minutes from time by firing low into the bottom corner for his first goal for Rotherham following a cross by O'Connor.