Simon Batt pounced after 27 minutes before Craig unleashed a speculative effort from 30 yards seven minutes later to dent Gillingham's survival hopes.
Danny Schofield added an impressive solo effort on the hour, and substitute Neil Harris headed in the fourth to seal a resounding victory.
Lively Gillingham striker Simeon Jackson threatened early on but the Lions stepped up a gear and Batt put them in front after being played through by Schofield.
Millwall were clearly not content with one goal and as they piled forward and Craig launched a looping volley into the top corner after Steve Morison's long throw ran loose.
The visitors responded but Millwall soaked up the pressure and Schofield jinked his way through after 60 minutes to fire in the third. The Lions were relentless, adding the fourth six minutes later, when Craig's corner was flicked across goal and Harris nodded in to complete the rout.