Stone extended the lead to 3-0 49 seconds into the third period, beating Kuemper glove side at the side of the net.
"It was a great play [by Eichel]. He drives a couple of guys to him and gets goalie chasing," Stone said. "I just banked it in. It's just great play by a great player. You have to be ready when he's got the puck because you never know where he's going to put it."
Wilson scored to make it 3-1 with 3:14 remaining in the game on a one-timer from the slot with Kuemper pulled for an extra skater.
The Capitals were outshot 28-9 in the first two periods.
"We just couldn't generate enough puck possession in the offensive zone," Washington coach Spencer Carbery said. "Our start was alright. We probably didn't do enough with those pucks early on that we could have turned into sustained pressure and delivery and shots on goals. In the second period, they took over and we weren't able to generate enough as we need to puck possession wise."
Marchessault scored an empty-net goal with 1:57 remaining for the 4-1 final.
NOTES: Washington forward Alex Ovechkin did not have a point and remains one shy of 1,500 for his NHL career. … Marchessault and William Karlsson combined on the same goal for the 136th time, tied with Marchessault and Reilly Smith for the most in Vegas history.