Brayden Point had a goal and two assists, and Alex Killorn scored twice for the Lightning (33-14-2), who have qualified for the playoffs for four straight seasons and won the Cup in 2020. Andrei Vasilevskiy made 36 saves.
"There's a high expectation in this organization to make the playoffs every single year, and you want it to become the norm," Tampa Bay coach Jon Cooper said. "These guys have done that, so I couldn't be more proud of them. To put yourself in a situation to compete for a Stanley Cup, you have to make the playoffs, and the guys have done that.
"Who knows where it's going to go from here, but it always feels good when you step over that hurdle."
Tampa Bay trails the Carolina Hurricanes by three points for first place and the Florida Panthers by one point for second place in the Discover Central Division. The Lightning and Hurricanes each have played two fewer games than the Panthers.
Patrick Kane had two assists, and Malcolm Subban made 15 saves in relief in the second and third periods for the Blackhawks (22-22-5), who were 1-for-7 on the power play. Kevin Lankinen allowed three goals on 11 shots in the first.
The Blackhawks are sixth in the eight-team Central and trail the fourth-place Nashville Predators by seven points for the final playoff spot from the division; Chicago has played two fewer games.
"If we're going to be competitive and win hockey games at the end, we're going to need to be better," Blackhawks coach Jeremy Colliton said. "I thought we had some bad things happen to us, some adversity, which certainly is part of it. But I'd like us to respond better, just being willing to compete defensively. But we weren't ready to compete hard enough away from the puck to give ourselves a chance to win."
Erik Cernak intercepted Riley Stillman's pass and scored on a breakaway to give the Lightning a 1-0 lead 28 seconds into the first period.