Teuvo Teravainen, recalled from the American Hockey League on Wednesday after Kane was placed on long-time injured reserve, scored a goal and Corey Crawford made 20 saves for his second shutout of the season in a 3-0 victory at BB&T Center.
Crawford, who ended a personal three-game losing streak, came in with a 3-0-0 record and a 1.18 goals-against average in his previous four appearances against Florida.
"[We've] just got to play hard, play the same way," Crawford said. "Stuff happens. It's a tough break for our team, but we've got to keep playing."
The Blackhawks beat the Panthers for the second time in three days to complete a home-and-home sweep and make it seven in a row in the series.
Brandon Saad had a goal and an assist for the Blackhawks, who haven't lost to the Panthers since March 8, 2011. Jonathan Toews scored an empty-netter with 46.8 seconds remaining, and Marian Hossa had two assists.
The Blackhawks (37-20-5) have won two in a row after a three-game losing streak.
"The test comes as you progress," Chicago coach Joel Quenneville said of moving forward without Kane. "Initially, you got a good response but sustaining it is the challenge."
The Blackhawks beat the Panthers 3-2 in a shootout at United Center on Tuesday after squandering a 2-0 period lead. They made sure there would be no comeback Thursday.
"The last two games were big wins for us," said Toews, who has a goal in each of Chicago's past three games. "They're hungry to win. I think we learned from our mistakes in the last game. We didn't want to let them back in the game. We had a 2-0 lead late in the game and just got after it."
Chicago played its first game without Kane, who is expected to miss 12 weeks after he sustained a broken clavicle Tuesday. Kane was injured when he slammed into the boards after being pushed in the lower back by Alex Petrovic. The Panthers defenseman was booed by the many Blackhawks fans at BB&T Center every time he touched the puck Thursday.
Goaltender Roberto Luongo made 26 saves for the Panthers (26-22-13), who lost their fourth consecutive game and missed a chance to tie the Boston Bruins for the second Eastern Conference wild-card spot for the Stanley Cup Playoffs. They trail the Bruins by two points and have played one more game.
"They played a really good game," said Panthers defenseman Brian Campbell, who was a member of the Blackhawks' 2010 Stanley Cup-winning team. "We got off to a slow start and then we started to get going. We had our chances as well to tie it up or get a few goals and see what happens there. There's some good things, but to win games like that we have to be going the whole game and I think we had a few lapses."
The Panthers have scored fewer than two goals in six of their past nine games, a stretch during which they're 2-5-2.
The Panthers began a season-long seven-game homestand that continues with an afternoon game against the Buffalo Sabres on Saturday, when veteran forward Jaromir Jagr, acquired in a trade Thursday, is expected to make his Panthers debut.
Florida could have used Jagr's offensive ability Thursday, particularly in the first half of the game. The Panthers were held to four shots on goal in the first 30 minutes, none of them in the first 10 minutes of the second period.
"That's not going to get you any goals," Bjugstad said. "That's not going to get you any wins if you're not getting pucks to the net. We didn't do a good enough job of that once again. We came on there at the end a little bit, but you can't start like that. To win you've got to shoot, and to score you've got to shoot. We didn't do that tonight."
Teravainen, considered one of Chicago's best prospects, opened the scoring 3:08 into the game after a turnover deep in the Florida zone. Teravainen took a backhand pass from Andrew Shaw near the right faceoff dot and skated toward the middle before quickly firing a wrist shot that beat Luongo to the short side.
"He's progressed," Quenneville said of Teravainen. "He's very astute, When he's got the puck he's got good awareness to his game. That was a nice play."
The Blackhawks had a great chance to pad their lead late in the first period when they had a 5-on-3 for 1:22, but they could muster little in the way of chances after Hossa hit the crossbar with a slap shot early in the two-man advantage.
Saad made it 2-0 at 3:07 of the second despite not getting a clean shot off on his one-timer off a feed from Duncan Keith. His off-speed shot fluttered past Luongo.
"He fanned on it," Luongo said. "I tried to get across as quick as I could there anticipating a hard one-timer and once he kind of fanned on it, I had trouble tracking it. I would have liked to make the save there."
The Panthers started applying pressure after the halfway mark of the second period, doubling their shot output with five in a three-minute span.
Campbell hit the post with a slap shot midway through the third period. Jonathan Huberdeau missed an open net from a sharp angle with about two minutes left after Luongo was pulled for an extra attacker.
"That's a big win," Crawford said. "We played playoff hockey there, played the puck in the right area, not forcing anything. We played well defensively, kept them to the outside for the most part and the score showed it."