A Jamie Vardy cross into the Charlton area eluded everyone, while Luke Moore nodded the ball tamely at Ben Hamer when free inside the area.
Morrison made Leicester pay when he headed home a Dale Stephens corner to put Chris Powell's side into the lead.
The away side were reduced to 10 men when James protested too vociferously to referee Darren Deadman for what he felt to be a push inside the Charlton box.
The hosts were 2-0 up when Kermorgant headed in at a corner, and, although Leicester felt their goalkeeper Kasper Schmeichel had been impeded, Deadman ignored their complaints.
Drinkwater reduced the deficit when he drilled the ball in from the edge of the box, but Schmeichel was the busier keeper in the latter stages, making three saves before Charlton celebrated victory.
Charlton manager Chris Powell:
"I'm pleased for my group of players. They have been down and it is a tough start but I told them there was no need to panic.
"We've had a lot of soul-searching between us all, a lot of hard work on the training pitch and changed our shape which has worked.
"When Yann plays like he did today then there are not many strikers better than him. I'm going to tell him there are 23 other teams called Leicester."
Leicester manager Nigel Pearson:
"There were certain things we were a bit disappointed with. In the first half we didn't find our rhythm and were slow to do things. We looked comfortable besides set-pieces. In terms of our own performance we were not at our best.
"But we could have got something out of the game. We pushed on, even with 10 men, but it wasn't to be. We didn't show the energy I would have liked. Unfortunately the talking points are not the players.
"The second goal was an absolute foul on Kasper. Liam Moore was also fouled. It was a foul on Matt, whether it is inside or out of the box is irrelevant. I had a very good view so the assistant has an excellent view but had no input."
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