Alex Kerfoot made it 4-0 at 5:18 of the third period, redirecting J.T. Compher's shot in front. Rantanen deflected in Barrie's point shot on a power play to push the lead to 5-0 at 7:53.
Strome cut it to 5-1 on a breakaway at 9:21, but Ryan Graves scored his first NHL goal at 13:28 to make it 6-1.
"It was a lucky bounce that came off a stick," Graves said. "It just popped out in front of me and I had an open cage. Even before I hit it, I was a little excited."
Graves was playing in his fifth NHL game after being recalled from Colorado of the American Hockey League on Dec. 26. He was acquired by the Avalanche in a trade with the Rangers on Feb. 26, 2018.
"It was fun, it was special for me," Graves said. "I played with a lot of those guys in camp for three years and in the American League, so coming against them it might be a little bit sweeter. Regardless of who we were playing, it's pretty sweet."