Chicago allowed at least one power-play goal in each of its prior four games.
"We got some great saves from [Lankinen] at key times there in that second period, but at the same time I really liked our third [period]," Blackhawks coach Jeremy Colliton said. "We beared down there and found a way to defend. I would've liked us to spend a little more time in the offensive zone, hold the puck down there, get some chances, draw a penalty. A lot of times that's how you close out a game, but we did have to defend quite a bit and we did a really good job."
Lankinen, a rookie, made 29 saves in his first NHL shutout, a 2-0 win at the Detroit Red Wings on Feb. 17.
Sergei Bobrovsky made 18 saves for the Panthers (20-9-4), who played without forward Aleksander Barkov for a second straight game because of a lower-body injury. They have lost three straight for the first time this season.
"We're trying to be too cute," Florida forward Jonathan Huberdeau said. "Just [need to] skate a little bit more. We look like we're not skating, so just do that. I feel that's what we've been doing all year and the last three games we've kind of stopped. That's not the way we have to play if we want to win."
Frank Vatrano appeared to give Florida the lead at 6:51 of the first period on a wraparound, but Lankinen made a save with his right skate then covered the puck with his blocker. The call of no goal was upheld after review.