Forsling made it 3-0 at 11:46 with a wrist shot from the point that deflected off the stick of Chicago forward Dylan Strome.
Bobrovsky made several big saves in the second period when Chicago had 16 shots on goal.
"He was locked in," Brunette said. "We knew they're a team with a lot of pride and it was a big night for them. They were going to try to win one for [Toews]. 'Bob' was outstanding."
NOTES: The Panthers are 28-6-0 at home. They set their previous record for home wins in 2017-18 when they were 27-11-3. … Florida has scored four or more goals in 26 of its 34 home games. … The Panthers have 98 points, tying for the second most in their history (1999-2000). They had 103 in 2015-16. … Florida center Joe Thornton became the sixth player in NHL history to play in 1,000 wins (regular season and Stanley Cup Playoffs combined), joining Nicklas Lidstrom (1,090), Chris Chelios (1,043), Patrick Marleau (1,029), Mark Messier (1,015) and Scott Stevens (1,007). … Blackhawks forward Patrick Kane's streak of 11 road games with an assist ended. It is a Chicago record. … Kane and Panthers forward Mason Marchment each had a game-high seven shots on goal.