The best-of-seven series is now tied at a game apiece. Chicago hosts Game 3 on Monday.
Tyler Johnson, Cedric Paquette and Nikita Kucherov had the other goals for Tampa Bay.
Brent Seabrook tied the game at three in the third for the Blackhawks. Teuvo Teravainen, on the power play, and Andrew Shaw had second-period goals for Chicago.
Andrei Vasilevskiy got the win in net, stopping all five shots he faced. Ben Bishop started for the Lightning and turned away 21-of-24 shots, but left the game in the third.
Corey Crawford made 20 saves in goal for the Blackhawks.
Both teams went 1 for 3 on the power play.