Lindholm scored the game-tying goal in the third period, and Jeremy Swayman made 30 saves for Boston, which is the No. 2 seed from the Atlantic Division.
The Bruins will play the Florida Panthers, who eliminated the Tampa Bay Lightning in five games, in the second round.
“When you’re not getting a lot of offensive chances, you lose your patience at times, and we talked about not losing our patience," Bruins coach Jim Montgomery said. “Being above, being behind, being physical and just being relentless with that kind of attitude, that’s why I was really happy to see the maturity of our group.”
William Nylander scored for Toronto, which was the No. 3 seed from the Atlantic. Auston Matthews had an assist in his return after missing Games 5 and 6 because of an illness and undisclosed injury.
“Obviously, this series [was] very close,” Maple Leafs coach Sheldon Keefe said. “That is the thinnest of margins you can get in Game 7 overtime. So, obviously very disappointing to not come on the right side of it. Loved how our team fought to put us in this position and compete and play in this game and have a chance to be one shot away.”