Skating down the left wing, Smith cut around Calgary defenceman T.J. Brodie and roofed a shot into the top corner over the outstretched glove of goalie Reto Berra.
The Flames held a 1-0 lead heading into the third period, but saw that evaporate as David Krejci scored a power-play goal to even the score before Smith's game-winning heroics.
The Bruins (21-8-2) have now won three straight games. After skating to a 3-2 win over the Pittsburgh Penguins at home on Saturday, the Bruins started their four-game road trip in Toronto on Sunday with a 5-2 victory over the Maple Leafs.
Jiri Hudler scored the lone goal for the Flames (11-15-4), who had won three of four heading into the contest.
Hudler also scored the game-winning goal in overtime on Saturday as the Flames beat the Oilers 2-1 in Edmonton. Calgary's leading scorer extended his point scoring streak to four straight games during which time he has two goals and three assists.
Boston goalie Tuukka Rask finished with 26 saves to improve his record to 16-7-2. Berra meanwhile stopped 22 shots.
Tuesday's game marked the return of former Flames captain Jarome Iginla to the Scotiabank Saddledome for the first time since he was traded last March 27 to the Pittsburgh Penguins for a first-round draft pick and a pair of college forwards.
After playing in 13 regular season games and 15 post-season contests with the Penguins, Iginla signed on as a free agent with the Bruins in the off-season.
The Flames carried the majority of the play in the opening frame when they outshot the Bruins 11-5. Iginla had two of Boston's shots and also whistled a one-timer wide of the net during an early man advantage for the Bruins.
With Boston defenceman Matt Bartkowski in the penalty box for holding, the Flames poured on the pressure during a late first-period power play, but Rask stood his ground to stop a trio of quality scoring chances.
After turning aside a shot fired his way by Mark Giordano, Rask also got a piece of a shot off the stick of Lee Stempniak and the puck trickled wide of the net. Mikael Backlund then one-timed a pass from Brodie, but Rask stuck out his pad to stop the shot and keep the game scoreless.
Hudler finally broke the scoreless deadlock at 5:17 of the second period when he snuck a snap shot from the top of the faceoff circle under Rask's glove and into the net.
Mike Cammalleri nearly put the Flames up 2-0 a short time later but his shot from the slot rang off the right post behind Rask.
After recording just four shots on net in the second period, the Bruins took the play to the Flames in the final frame as they outshot them 15-6.
Krejci tied up the game at 1-1 at 13:49 of the third when he tipped a point shot fired by Torey Krug past Berra.
Notes: Iginla's last game at Saddledome as a member of the Flames was on March 24 when he scored the game-winning goal in a 3-2 triumph over the St. Louis Blues. Iginla played one more game — a 2-0 road loss to the Chicago Blackhawks two nights later — before being traded to Pittsburgh. … Giordano, who succeeded Iginla as Flames captain this season, played his fourth straight game after missing 18 contests with a broken ankle. He recorded an assist on Hudler's goal to give him 12 points (three goals, nine assists) in 12 games.