Kane gave Detroit a 1-0 lead 37 seconds into the second period with a backhand from the right circle.
Cirelli tied it 1-1 with a short-handed goal at 8:36, scoring on a wrist shot from the top of the right circle.
"It's the little things," Cirelli said. "Give credit to them, they came out, played hard and capitalized on the chances that they had. We'll watch some video tomorrow and we'll be better."
Cirelli had two goals disallowed in the period, including one on the previous play following video review.
"That's why they have video," Cirelli said. "From the standpoint I saw, I thought it was in under his pad. At the end of the day, it is what it is."
Fabbri put the Red Wings back ahead 2-1 at 3:40 of the third, beating Vasilevskiy with a backhand off a pass from Compher.
"Our guys were really battling," Detroit coach Derek Lalonde said. "This was an unbelievably difficult road trip, at [the Carolina Hurricanes], at [the Florida Panthers], at Tampa. We pointed in three of our last four on the road. I was really proud of the group. We’ve had a lot of adversity all year, ups and downs, and we’ve just kept in the fight, kept battling."
NOTES: Lightning forward Nikita Kucherov had an assist to give him 127 points (42 goals, 85 assists) this season, tying Nathan MacKinnon of the Colorado Avalanche for most in the NHL. ... Lyon was 0-8-2 in his previous 10 starts.