Paul Pierce had 21 points, six rebounds and five assists. Kevin Garnett added 21 points and 13 rebounds for Boston, which won its sixth consecutive game.
Rondo, a 6-foot-1 point guard, added eight rebounds and seven assists, running the Celtics' offense to a season-high point effort.
Corey Maggette paced the Warriors with a season-high 32 points and Stephen Jackson had 30. Golden State lost its fourth straight.
The contest featured the NBA's leading defensive team, Boston, against one of the league's highest-scoring offenses.
The lead changed hands seven times in the final quarter before Boston took it for good on Tony Allen's three-point play, making it 103-102 with 6:43 remaining. Allen collected Garnett's airball in the lane, scored on a layup and was fouled.
After Maggette missed a jumper on the other end, Garnett converted a three-point play on Boston's next possession to increase it to 106-102.
Rondo's follow pushed Boston's lead to six and Ray Allen nailed a 3-pointer from in front of the Warriors' bench, making it 113-104 with 3 1/2 minutes left.
Boston, which trailed 67-54 at halftime, opened the second half with a 22-10 run to climb back into it. Pierce's turnaround jumper in the lane gave the Celtics an 84-83 edge, their first lead since midway into the second quarter, and they led 86-83 after three.
Boston started as if it was going to be a blowout win, grabbing a 30-20 lead nearly eight minutes into the contest, before the Warriors started rolling.
Trailing 40-30 early in the second, Golden State, which entered as the league's third-best scoring team at 103.3 points per game, outscored Boston 28-8 over a 6:18 stretch en route to its 13-point lead at intermission. Maggette scored 13 in the spree.
Notes:@ Boston's previous season high was 118 in a victory at Toronto on Sunday. ... The Celtics had a moment of silence for Helen Heinsohn, wife of Hall of Famer and team broadcaster Tommy Heinsohn, before the game. She passed away Monday after a battle with cancer. ... Boston had its highest-scoring first quarter of the season (35). ... The Warriors then held the Celtics to just 19 in the second, the fewest Golden State has given up this season. ... Boston coach Doc Rivers was whistled for a technical in the final minutes of the second.