Colorado scored 4:38 into the second period on a goal originally credited to rookie Nathan MacKinnon, when it looked as though he tapped in a pass from Mitchell. But the goal was later awarded to Mitchell after the puck appeared to hit off the stick of Jets defenseman Zach Bogosian.
The lead didn't last long as Byfuglien scored twice in a span of 1:48. He tapped his first goal past Varlamov on a power play. Later, Byfuglien bounced a puck off Varlamov's left skate from near the boards behind the net.
Benoit tied it with 12 seconds remaining in the second on a slap shot from near the blue line.
It was a frenetic first period that featured no scoring but plenty of big hits and a penalty shot by Jim Slater after Marc-Andre Cliche hooked him from behind. Slater couldn't capitalize, though, lining his shot into Varlamov's glove.
Varlamov later turned back Evander Kane on another breakaway attempt. The Jets were flummoxed by Varlamov all period, even running into the Colorado goalie twice and drawing penalties.
The Avs were on the power play four times in the first period, but couldn't sneak anything past Montoya, who gave Ondrej Pavelec the night off.
Colorado lost Parenteau in a collision near the blue line with Mark Stuart less than four minutes into the game. After a quick rest, Parenteau momentarily returned to the ice to test out the knee before heading into the dressing room.
"He was in pain, but you know P.A.," Roy said. "He's a great team guy, and he wanted give it a try."
NOTES: Jets F John Albert left in the second period because of an upper body injury and didn't return. ... F Bryan Little recorded two assists, giving him 52 points for the season, which is a career high. ... Varlamov earned his 32nd win of the season.