Lucic tied the game with 67 seconds left in the third period.
Indeed, both teams needed a win. The Bruins, after being routed by Buffalo, came into the game just 5-6-1 in their previous 12 games. They peppered Pekka Rinne with 41 shots through overtime and Nashville blocked another 29.
Fisher gave the Predators their first lead at 3-2 with 3:32 remaining when he skated around the net to get his own rebound on a shot that skidded through the crease and beat Thomas with a sharp backhand.
But Lucic tied it on a power play, picking up a rebound low on the right side after a shot by Rich Peverley was ticked aside and flipped it into the net with Rinne down in the crease.
The Bruins, testing Rinne all day, tried to sneak the game-winner through in the last seconds of regulation. Brad Marchand had two good looks in a row but both were stopped -- the second by the defenseman Weber, who slipped in behind his own goaltender to knock the puck out of mid air.
Earlier, with the Bruins shorthanded, Bergeron opened the scoring with a shot from the right side after a drop pass from Marchand late in the first period.
Weber scored with a slap shot from high on the left side during a power play in the second period but Boston regained the lead on Paille's backhand goal in front early in the third period. Hornqvist then tied it again midway through the third, jamming in a loose puck from in front.
The teams have historically been evenly-matched. They had split the previous 10 games entering Saturday...Although they have lost four of their last five, the Predators are 14-4-2 in their last 20.