St. Louis was the 10th player to score in a game that saw the Lightning outshoot the Blackhawks 43-25.
Steven Stamkos was the only one with two goals to his credit and his second one, coming with 2:29 left in regulation, boosted Tampa Bay into a 5-4 lead. Jonathan Toews then forced overtime by scoring with 1:49 to go in the third.
The defending Stanley Cup champion Blackhawks had won their previous two games and suffered their third overtime loss of the season.
Ben Bishop gave up the five Chicago goals, but managed 38 saves to improve his record this year to 6-1.
Chicago twice came from behind and took a 4-3 lead on a goal by Andrew Shaw on the power play 1:33 into the third.
Khabibulin was in goal for all of the Tampa Bay scores and finished with just 19 saves.