The Hammers had to respond in positive fashion after their midweek thrashing at Newcastle. Grant made eight changes for the game, opting for a young side that played with plenty of hunger.
Jonathon Spector continued his good recent form with another first-half goal before second half substitute Freddie Piquionne scored an injury time goal to seal the Hammers passage into the draw for the Fourth round.
"I am very pleased with the team," said Grant.
"They were very good, especially in the first half and if we had taken 20 per cent of our chances the score would have been high. I am pleased overall to be in the next round and that we could give a chance to some new players."