Rotherham led in the eighth minute. Marcus Marshall’s cross evaded everyone in the penalty box and as the ball bounced free Gareth Evans fired home.
But the home side were pegged back in the 21st minute when slack marking in the Rotherham defence allowed Scott Doe to head home Gavin Tomlin’s corner.
But two goals in nine minutes from Grabban put Rotherham back in the driving seat. After 29 minutes he headed home from Marhsall’s high cross and nine minutes later he reaped the reward for some great work by Evans.
Evans robbed Tomlin out left and cross for Grabban to turn and shoot past Chris Lewington in the Dagenham goal.
Two half time substitutions put more life into the visitors after the break and Oliver Lee twice went close, first hitting the bar and then having a shot well saved by Conrad Logan.