Paul Pierce led the Celtics with 29 points and Kevin Garnett added 26 points and 16 rebounds. James paced the Cavaliers with 35 points.
The series moves to Cleveland on Friday with the top-seeded Celtics looking for their first road win of the playoffs to clinch the conference semifinal.
The winner will meet the Detroit Pistons for a place in the NBA Finals.
The Lakers head to Utah to play the Jazz in Game 6 on Friday.
Cleveland coach Mike Brown said Boston's defensive pressure in the third quarter was the turning point.
"In the third quarter they turned up their aggression and I think that was the difference in the ball game," Brown told reporters.
"In our first three or four possessions in the third quarter we had turnovers and that set the tone for the Celtics, set the tone for the crowd. It was a rough go from there."
Besides saluting Garnett and Pierce, the Cavs coach praised Boston point guard Rajon Rondo, who hit back-to-back 3-pointers during the Celtics' run to end the first half.
Garnett and James agreed about the role played by Rondo, who had 20 points and dealt out 13 assists, two more than the Cavs as a team.
"Rondo hit some big shots for us, got us into a flow and we carried it into the third quarter," Garnett said.
James, who had shot only 26 percent from the floor over the first four games, was 12-of-25 but had only three rebounds. He also singled out the Boston point guard's contribution.
"Rondo tonight was definitely the player of the game," James said.
The Cavaliers coach was not dispirited.
"The series is not over until somebody has won four games," Brown said. "We just head back to Cleveland, lace them up for the next game and get ready to rock and roll for 48 minutes."
(Agencies via China Daily May 16,2008)