Reinhart made it 4-1 at 7:48 with a power-play goal when he tipped Montour's shot from the point before Eetu Luostarinen made it 5-1 with another power-play goal at 9:25.
Nick Cousins pushed it to 6-1 at 15:38 when he scored right after Florida killed off a two-minute 5-on-3 power play.
Forsling extended the lead to 7-1 at 17:00.
Greig scored at 16:18 of the third period for the 7-2 final.
Lyon is 5-0-0 with seven goals allowed in his past five starts.
"One guy that was dialed in from start to finish straight through regardless of what was going on in the game was Alex, and he was good at all areas," Panthers coach Paul Maurice said. "I'm happy for him because he's worked really hard to be that good from his first tour up (from the American Hockey League) and then coming back in. He comes to the rink at even keel but works very, very hard at his game. So, I'm happy for him because he's earned it. It hasn't been easy and good for him, and then, of course, good for us."
NOTES:Ottawa forward Austin Watson left the game in the second period with a lower-body injury. There was no update. … The Senators (88) and Panthers (78) combined for 166 penalty minutes. There were eight majors and 10 misconduct penalties, including game misconducts against Smith, Senators forward Brady Tkachuk, and Panthers defenseman Marc Staal. … Montour had four points (one goal, three assists) in a 5-3 win at the Anaheim Ducks on Nov. 6. … Along with Montour's four points and the two each for Ekblad and Forsling, Staal and Radko Gudas each had an assist to give the Panthers a franchise-record 10 points from their defensemen. … Matthew Tkachuk has an NHL career-high 105 points (39 goals, 66 assists). He had 104 (42 goals, 62 assists) with the Calgary Flames last season.