Tuukka Rask made 24 saves for Boston.
Brian Boucher stopped 24 shots for the Flyers.
Game 3 is Wednesday night in Philadelphia.
Miroslav Satan had a goal and two assists for Boston, and Johnny Boychuk also scored for the Bruins, the No. 6 seed in the East that inherited home-ice advantage for the second round when the conference's top three teams were eliminated in the opening round.
Danny Briere scored for the Flyers, and assisted on Mike Richards' goal for his fourth straight multiple-point game of the playoffs.
It was 1-1 after one period and 2-2 after two. It stayed that way until Lucic got the puck between the circles, turned around and slapped a shot past Boucher. It was Lucic's first goal of the playoffs, his first in nine games and just his second in 18 games, dating to March 25.
The Flyers pulled Boucher in the final minutes for an extra skater, but the best scoring chance was a shot by Boston that was picked off the post by Philadelphia defenseman Chris Pronger to keep it a one-goal game.
Boston has won seven in a row at home after winning just three of their last 17 in the regular season after the New Year's Day Winter Classic against the Flyers at Fenway Park.
The Bruins led by two goals three times in Game 1 on Saturday, but the Flyers tied it with 3:22 to force overtime. Marc Savard, who hadn't played in almost two months because of a concussion, scored the game-winner to give the Bruins the early lead in the series.
Boston came out intent on holding serve at home.
The game started in chippy fashion, and both coaches were warned 18 seconds in when a scrum developed and the players pushed after the whistle. The Bruins scored first for the second straight game when Boychuk beat Boucher at 5:12 of the first period.
This time, the Flyers came right back, tying it with 3:06 to play. The Bruins repeatedly failed to clear the zone, and Richards took advantage.
Boston made it 2-1 on Satan's goal midway through the second, but Philadelphia tied it with 24.8 seconds left in the period when Briere found the upper corner on Rask's stick side.
NOTES: Because of the water main break outside of Boston that forced residents to boil drinking and cooking water, the TD Garden brought in 13,520 bottles of water and 18,720 20-ounce bottles of soda to sub for the fountain drinks usually available at the concession stands. Sanitizer was provided for washing hands, and a 40-foot freezer truck was brought in with ice made outside the affected area. ... Boston's Patrice Bergeron was 9-0 in faceoffs in the first period. ... Satan has a five-game point streak, with four goals and four assists. ... Briere has nine points (four goals, five assists) in the last four playoff games.
