Simeon Jackson, Luis Cumbers and Mark Bentley got on the scoresheet for the Gills but victory was overshadowed by the ankle injury sustained by defender King.
Stimson said: "Unfortunately we've picked up another bad injury. If I'm honest it's a nightmare.
"He is a big player for us and we all know how important he was for the team last year.
"He went over on his ankle and it is absolutely huge. We will shut him down for a couple of days and see where we go from there.
"He is someone who will play if he has half a chance but we don't want to take too many gambles early on."