Jaromir Jagr, Aleksander Barkov and Jason Demers scored for Florida (12-11-3), which is 1-2-2 through the first five games of its six-game road trip. With his goal, Jagr moved to within six points of Mark Messier for second on the all-time scoring list with 1,881 points.
Panthers goalie Roberto Luongo made 32 saves and moved into sole possession of fifth place on the all-time games played list with 944, passing Curtis Joseph.
WATCH: All Panthers vs. Bruins highlights
Florida trailed by one goal twice in the third period, but Demers' goal with 1:29 remaining helped the Panthers earn a point in the standings. Florida is 1-7-3 when trailing after two periods.
"That is positive. It shows that our team is getting a little bit more confidence and not giving up on games whenever we're down," Panthers forward Vincent Trocheck said. "So the fact that we came back a couple times shows some strength in this team. I'm proud of us for that. But at the end of the day, we've got to be able to close out games and we didn't do that."
Schaller gave the Bruins a 1-0 lead at 18:32 of the first period.
Florida tied it 1-1 on Jagr's goal at 9:44 of the second, but Pastrnak buried a one-timer from the slot at 16:37 to put the Bruins back in front.
Barkov tied it 2-2 at 7:54 of the third period with a wrist shot from between the circles.
Backes tipped Ryan Spooner's shot from the right point past Luongo for a 3-2 lead, but the Panthers salvaged a point on Demers' goal at 18:31.