Millers striker Michael Smith wasted an opportunity to put the visitors in front in the 18th minute when his penalty was brilliantly saved by Gills goalkeeper Jack Bonham.
However, Smith opened the scoring barely 60 seconds later, capitalising on a defensive mix-up between Bonham and Connor Ogilvie to slot into an empty net.
Managing the inconsistent Gills against one of his former clubs, Steve Evans was booked by referee Lee Swabey for dissent after 25 minutes.
Leading goalscorer Crooks then doubled his side's advantage on the stroke of half-time, ending a fine solo run through midfield with a 35-yard chip over the Bonham.
And he added his second two minutes from time, firing home from close range after meeting Carlton Morris' through ball.
Brandon Hanlan fired just wide on the half-volley midway through the opening half for the hosts before Rotherham goalkeeper Dan Iversen denied Mark Byrne a late consolation.