Hedman carried into the left circle and sent his pass through the middle just beyond defenseman P.K. Subban's stick to Johnson converging on Price from the right.
The Lightning won their fifth straight playoff game and will go for a sweep of the Eastern Conference semifinal series on Thursday night in Tampa.
Alex Killorn scored a first-period goal for the Lightning, who were outshot 31-19. Price finished with 17 saves after giving up six goals in Game 2 in Montreal.
The Lightning won the opener on the road in double overtime, then scored four power-play goals en route to winning Game 2. Steven Stamkos contributed the go-ahead goal and two assists after going 11 consecutive playoff games without scoring — a stretch dating back to Montreal's four-game, first-round sweep of Tampa Bay a year ago.
Montreal coach Michel Therrien talked about the need for his team to play more disciplined. The Canadiens killed off two penalties — one on Tomas Plakenic for tripping Bishop — and Price made a pair of nice saves in the first five minutes, rejecting J.T. Brown's back-hander and Valtteri Filppula's wrist shot from point-blank range on one sequence.
Killorn scored his third of the playoffs by beating Price from the lower right circle after taking a pass from Stamkos. Meanwhile, Bishop was not tested much in the first two periods, even though the Canadiens outshot the Lightning 16-9.
The closest the Canadiens came to scoring before Gallagher tied it midway in the third was Subban's first-period shot that hit the post. Jeff Petry struck the post nine minutes into the third.
at Washington 2, New York Rangers 1: Rookie Andre Burakovsky scored his first two playoff goals and Braden Holtby saved a penalty shot, giving the Capitals a 3-1 lead in the Eastern Conference semifinals.
Burakovsky tied the game in the second period, then put Washington ahead 24 seconds into the third.
With 12 minutes left in regulation, Holtby — who finished with 28 saves — flicked his glove to catch Carl Hagelin's penalty shot and preserve the lead.
The Capitals can close out the Presidents' Trophy-winning Rangers in the best-of-seven series and advance to the conference finals for the first time in Alex Ovechkin's career by taking Game 5 in New York on Friday night.
The Capitals won a fifth consecutive home game in the same postseason for the first time, according to STATS. This marks the Rangers' 11th consecutive playoff game, dating to last season, decided by one goal, extending their NHL record.