It was quite the night for Bickell, who had his wife and daughter watching from the stands.
The Hurricanes were eliminated from postseason contention on a night when they took their third straight loss.
Eddie Lack made 23 stops for the Hurricanes in his first start since being taken to the hospital with a strained neck last week.
The Hurricanes have earned a point in 12 straight games.
Andreas Athanasiou crashed into Eddie Lack as he scored in overtime Monday night
Cam Ward stopped 33 shots.
Joakim Nordstrom and Elias Lindholm scored for the Hurricanes, who have lost three of five.
Joakim Nordstrom also scored for the Hurricanes, and Cam Ward made 23 stops.
Carolina is tied with New Jersey for last place in the Metropolitan Division.
Tyler Johnson and Nikita Kucherov also scored to help the Lightning improve to 7-1-2 in the last 10 games.