With the win, the Spurs avoided an 0-3 hole from which no NBA team has recovered.
New Orleans, which outscored San Antonio 65-35 in the third quarters of the first two games, and led, 56-54, at halftime of Game 3, was outscored, 29-22, in this third period.
The Spurs led, 83-78, entering the fourth quarter. New Orleans pulled the score to 90-88 before the Spurs put the game away with an 11-0 run.
Pierce scored 19 points, Kevin Garnett added 13 with 12 rebounds, and Allen broke out of a seven-quarter scoring drought with 16 points to help the Celtics take a 2-0 series lead with the win at Boston.
One game after going two for 18 from the field, James missed his first three tries and finished with 21 points on six-for-24 shooting.
"I'm a little shocked that he's eight for 42, but this is what we work on. We work on trying to contain him," said Pierce, who made seven of 13 shots after going two for 14 in Game 1. "LeBron is what makes them go. And if we can somehow control him, we control their team. And with the help of the guys around me, we've been able to do that."
This time, the poor shooting was contagious: The Cavaliers shot 35.6% in the game, making only 11.8% in the second quarter as Boston turned an eight-point deficit into a nine-point lead. From early in the second quarter to early in the third, a span of 13:41, Boston outscored Cleveland, 36-10.
"Being down 0-2, that's a tough hole to dig yourself out of. But if we want to win the series we've got to do it," James said, noting the Cavaliers lost the first two games to Detroit last year but won four straight to reach the NBA Finals.
Cavaliers forward Ben Wallace left 3:40 into the game because of dizziness he blamed on allergies and did not return.