The Bruins live to play another day after a 2-1 victory in Florida.
Boston was brought to the brink, but now trail the Panthers 3-2 in the second round of the Stanley Cup playoffs.
The Bruins got on the board first with a first-period goal from Morgan Geekie.
Sam Reinhart tied it up for the Panthers in the second period, but Charlie McAvoy responded with what turned out to be the winning goal about four minutes later.
Boston will need to win Game 6 at the TD Garden on Friday to force a Game 7 in Florida on Sunday.