The visitors seldom threatened the hosts' rearguard and Griffiths rounded off the scoring from the penalty spot 25 minutes from time.
The home side dominated the opening exchanges and went ahead as early as the fourth minute when Griffiths swiveled on the edge of the area before firing past Stuart Nelson in the Gillingham goal.
Martin Allen's men struggled to assert themselves throughout the first half and it got worse for away side when Evans headed home a second on 24 minutes.
Zeli Ismail, who was handed a starting berth for the visit of the Gills, vindicated his manager's decision by playing a key role in the team's third six minutes later, passing across the face of goal for Sako to tap home from close range.
However, Griffiths put the result beyond doubt midway through the second half by converting from the penalty spot.