A hugely disappointing first half only came to life in the final minute when the home fans finally had something to cheer.
A flowing move involving Alex Revell, Grabban and Danny Schofield ended with Schofield shooting just wide.
Earlier, James Hanson tested Rotherham's on-loan debutant goalkeeper Rhys Taylor with a shot from the edge of the area and then Hanson got his head to Craig Fagan's corner but couldn't direct his header on target.
It was not until the 57th minute that Rotherham managed a shot on target when Schofield's shot was well saved by Jon McLoughlin.
And six minutes later Grabban grabbed the lead for the hosts. Substitute Jon Harley's high cross was not held by McLoughlin and with the keeper grounded Grabban slammed the ball home.
Grabban added a second from the penalty spot in the 67th minute after McLoughlin charged off his line and bowled over Sam Wood, who was clean through on goal.
And worse was to follow for McLoughlin seven minutes later as substitute Brett Williams spotted the keeper off his line and unleashed a 40-yard shot, which the back pedalling shot stopper caught but then carried over his line.