Barkov had an assist Saturday in his return after missing six games with a lower-body injury.
"Actually, the first game I didn't feel that good," Barkov said. "Obviously, I was happy to be back. That's why I kind of got through the game. I didn't feel that good, but the team played well, so it was easy to come back. I felt a little better today, and playing with these linemates and this team, it makes it easier for me."
Frank Vatrano made it 2-0 at 8:00 of the third period with a wrist shot on a 2-on-1 after he stole the puck in the neutral zone.
Vatrano has scored in three straight games, with each goal in the third period. Ten of his 13 goals this season have come in the third period or overtime.
"I don't know, it's just the way that goals are falling for me right now," Vatrano said. "Tonight, we played a patient game. We didn't chase it. We stayed right with it for the full 60 minutes and got rewarded with it."