The Bruins will play the Philadelphia Flyers in the Eastern Conference semifinals for the second consecutive year.
Tim Thomas stopped 34 shots for the Bruins, who recovered after losing the first two games of the series at home. Boston had never won a playoff series after trailing 0-2 in 26 tries.
Carey Price stopped 30 shots for Montreal, which erased deficits of 2-0 and 3-2 in Game 7.
Horton scored with a slap shot off a pass from Milan Lucic, setting off a celebration on the Bruins bench and in the stands. It was Boston's third overtime win in the series, including Game 5 on Saturday night when Horton scored 9:03 into the second extra period.
Johnny Boychuk and Mark Recchi scored in the first 5:33 of Game 7 to give the Bruins a 2-0 lead. But Yannick Weber made it a one-goal game with a power-play goal in the first. Tomas Plekanec tied it in the second with an unassisted, short-handed goal.
After Chris Kelly scored with just under 10 minutes left to give Boston a 3-2 lead, P.K. Subban tied it in the final two minutes — again on the power play.
The Bruins were 0 for 21 on the power play in the series.
But it doesn't matter.
They will open the next round in Philadelphia with a chance to avenge last year's epic collapse against the Flyers. Boston led that series 3-0 before Philadelphia came back to force a decisive game; in Game 7 in Boston, the Bruins took a 3-0 lead before losing 4-3.
That was the second straight year that the Bruins lost a Game 7 at home.
This time, they made sure it wouldn't happen again.
The Canadiens won the first two games in Boston to swipe the home-ice advantage, but the Bruins came back to win three straight — including the first two in Montreal, and then Game 5 at home. The Habs won Game 6 on Tuesday night to force a seventh game in Boston.
The Bruins wasted another early lead on Wednesday, jumping out on a slap shot by Boychuk and a wrister by Recchi from the slot that beat Price on the stick side. Montreal coach Jacques Martin took his timeout, and the Canadiens seemed to regroup.
After Michael Ryder was sent off for hooking, Weber scored a power-play goal by converting a cross-ice pass from Michael Cammalleri midway through the first.
Five minutes into the second, with the Canadiens down a man, Plekanec stole the puck from Recchi and broke in alone to wrist it past Thomas and tie it 2-2. But Kelley slid a rebound back under Price with 9:44 left in the third to put Boston back on top.
Montreal tied it after Patrice Bergeron was sent off for whacking James Wisniewski in the face with 2:37 left. The Canadiens set up the power play in the Boston zone and worked the puck around to Subban, who slapped it over Thomas' glove.
Notes
Lucic was back in the game, one day after he was given a major for boarding and a game misconduct in Game 6. … Canadiens center Jeff Halpern went to the ice after taking a shoulder from Andrew Ference in the corner with 11:30 left in the third. He was attended to by a trainer and helped off the ice, apparently woozy. … TV showed Thomas and Price tapping each other with their sticks as they left the ice at the end of the second period.