The Lightning let a two-goal advantage get away but Dwayne Roloson was perfect in the shootout to help Tampa Bay halt a four-game losing streak and move into a fourth-place tie with Boston in the Eastern Conference.
Chicago is tied for fourth in the West with Calgary, which earned two points with a shootout victory over Dallas. The Blackhawks moved within five points of Detroit for the lead in the Central Division.
Steven Stamkos boosted his NHL-leading goal total to 42 while Tampa Bay was building a 3-1 lead but scores by Patrick Sharp midway through the second period and Jonathan Toews early in the third allowed Chicago to tie it.
Roloson made 28 saves while Corey Crawford stopped 27 shots for the Blackhawks.