Salomon Kalou headed in the second just after half-time before Steve Sidwell's swerving strike quickly made it 3-0.
Kalou completed a convincing win by crashing home a drive.
Chelsea's confident display did not stop their fans chanting ex-boss Jose Mourinho's name but Grant will be relieved to have posted his first win in such convincing fashion.
Hull battled manfully throughout but they never really looked capable of an upset.