The Bruins lead the best-of-seven series, 3-2, with a chance to eliminate the Canadiens in Montreal on Monday night. Game 7 would be Wednesday night back in Boston.
Carl Soderberg and Loui Eriksson also scored, and Tuukka Rask stopped 29 shots for Boston. He extended his shutout streak to 122 minutes, 6 seconds before Brendan Gallagher scored to make it 3-1 on a power play with 5:21 left in the second period.
Carey Price made 26 saves for Montreal. P.K. Subban had a late goal power-play goal.
The Bruins had not scored a power-play goal in the playoffs against the Canadiens in 39 tries over 14 games dating to 2009.
Soderberg gave Boston the lead with 6:40 left in the first, and it was still 1-0 at the end of the period when Tomas Plekanec was penalized for interfering with the goaltender. Just 64 seconds after the break, Smith redirected Dougie Hamilton's shot past Price to make it 2-0.
Sixteen seconds later, Plekanec was sent off again — this time for high-sticking. It only took 6 seconds into the power play for the Bruins to make it 3-0 on a backhand crossing pass from Torey Krug to Iginla.
Plekanec set up Gallagher to cut the deficit to two goals with 5:21 left in the second period, but Eriksson snapped in the rebound of Game 4 hero Matt Fraser's shot with just under 6 minutes left in the game to make it 4-1.
Montreal pulled Price for most of the last 5 minutes, and Subban scored on a 6-on-4 power play. But the Canadiens could not get any closer.