Marco Sturm, Phil Kessel, Brandon Bochenski and Stanislav Chistov had Boston's other goals. The Bruins have won eight of 10 to move within five points of Carolina for the final Eastern Conference playoff berth.
Boyes scored midway through the first and early in the second to give Boston a 3-1 advantage. Thomas stopped an in-close shot by Ruslan Fedotenko halfway through the second.
Dan Boyle and Filip Kuba scored for the Southeast Division-leading Lightning, who lost for just the fifth time in 21 games. Tampa Bay has a one-point lead over second-place Atlanta.
Sturm put the Bruins ahead 1-0 at 1:46 of the first with his 20th goal this season and seventh in his last seven games.
Boyle tied it at 1 during a power play at 5:29. Vincent Lecavalier (seven assists, 13 points) and Brad Richards (nine assists, 11 points) both extended their point streaks to seven games by assisting on the goal.
Boyes made it 2-1 on a rebound goal at 9:41. After the goal, Lightning coach John Tortorella pulled goalie Marc Denis and replaced him Johan Holmqvist.
Denis allowed two goals on seven shots. Tampa Bay had just one shot during the same stretch.
Boston went up 3-1 on Boyes' second of the game during a 2-on-1 at 3:58 of the second. He scored off a pass from Marc Savard, who had three assists.
Savard has 10 assists and 12 points during a seven-game point streak.
Kessel extended Boston's lead to 4-1 with 7:19 left in the second on his first goal in 16 games.
Bochenski and Chistov scored third-period goals, helping the Bruins sweep the four-game season series with Tampa Bay. Bochenski also had two assists.
Kuba made it 6-2 late in the third.
Notes: Bruins C Patrice Bergeron (lower body) skated before the game, but was out of the lineup for the fifth straight game. ... Tampa Bay C Andreas Karlsson, who hurt his left index finger in Thursday's game at Atlanta, didn't play. ... Boston RW Glen Murray (groin) missed his second straight game.