Patrice Bergeron scored for the seventh straight game midway through the second period to give Boston a 3-2 lead, but the Flyers' Vincent Lecavalier swatted home a bouncing puck with 24.1 seconds left in regulation to force overtime.
After an entertaining extra session failed to produce a winner, Lecavalier came up empty to open the shootout before Bergeron and Claude Giroux exchanged markers.
The next six shooters were all turned aside before Smith skated in and used a series of dekes to fool Steve Mason before stuffing the puck into the back of the net for the victory.
Zdeno Chara and former Flyer Andrej Meszaros supplied Boston's other goals, while Tuukka Rask recorded a career-high 49 saves for the Bruins, who have taken at least one point in each of their last 16 road games (13-0-3), also a franchise record.
Boston, which leads the NHL with 110 points, also extended its point streak to 16 games, improving to 15-0-1 since their last regulation loss on Mar. 1 against Washington.
Lecavalier also lit the lamp in the first period for his 400th career goal, while Kimmo Timonen notched the other goal for Philadelphia, which picked up a point to move into a tie with the New York Rangers for second in the Metropolitan Division. The Rangers visit Edmonton later Sunday.
Mason made 27 saves in defeat.