Roloson was pulled in the first period after he allowed three goals on nine shots. Smith came on and made 21 saves as the Lightning avoided dropping into a big hole against the surging Bruins. Boston will host Game 5 on Monday.
Teddy Purcell scored twice in the second period when the Lightning tied it at 3. Tampa Bay also got a goal from Sean Bergenheim, who leads the NHL with nine playoff goals after scoring 14 times during the regular season.
Martin St. Louis sealed the win in the final minute with an empty-net goal.
Gagne gave the Lightning a 4-3 lead when he beat Tim Thomas from the right circle 6:54 into the third period after Tampa Bay left wing Ryan Malone stole the puck near the blue line. The Lightning outshot the Bruins 9-1 through the first seven minutes of the period after scoring three unanswered goals in the second.
Smith replaced Roloson with two minutes to go in the first and then made 13 saves in the second en route to his first NHL playoff win in his second career postseason appearance — both this series in relief of Roloson.
Patrice Bergeron had two goals during a three-goal first that put the Bruins up 3-0. The alternate captain missed the first two games of the series because of a concussion sustained when he was hit by Philadelphia's Claude Giroux in the final game of the second round.
Michael Ryder also scored for the Bruins, who had won two straight in the series.
Purcell cut the Lightning's deficit to 3-2 with a pair of goals midway through the second. The first came on a backhander from the slot at 6:55. The right wing followed that with a goal from the right circle 1:03 later.
Bergenheim outworked Boston defenseman Tomas Kaberle for the puck behind the net and scored from below the right circle to tie it at 3 with 9:07 left in the second.
It was Tampa Bay's second quick three-goal surge in the series. The Lightning scored a team-playoff record three times in a 1:25 spurt of their 5-2 win in Game 1.
Thomas, coming off a 2-0 victory in Game 3, had a scoreless stretch of 93 minutes, 40 seconds snapped when Purcell scored his first.
Bergeron put the Bruins up 1-0 11:47 in after he got possession of the puck near the post and put a shot past Roloson. The goal came after Lightning defenseman Victor Hedman made an ill-advised pass from behind the net that got past teammate Brett Clark.
Ryder got a break on his goal at 16:34 when his pass toward the slot was deflected by Tampa Bay defenseman Mike Lundin and past Roloson.
The Lightning not only failed to score on a power play, but allowed Bergeron's short-handed goal late in the first. The center made it 3-0 with 2:02 left in the period after stealing a pass by Lightning center Steven Stamkos in the neutral zone and firing a shot from the top of the left circle past Roloson, who was then removed from the game.
Bergeron has four goals and 14 points in 13 playoff games this season.
Tampa Bay right wing Steve Downie received a roughing penalty and 10-minute misconduct during a scrum as the first period ended. Tampa Bay's Marc-Andre Bergeron and Boston's Rich Peverley both got fighting majors.
Notes:
Tampa Bay D Pavel Kubina, out since the first game of the conference semifinals against Washington when his head went into the glass on a hit, missed his seventh straight game. He hasn't resumed skating and there is no timetable for his return. … Boston fell to 7-1 in the postseason when scoring first. … Smith also replaced Roloson in Tampa Bay's 6-5 loss to Boston in Game 2.