After falling behind by 13 points, the Lakers rallied to score nine in a row until Celtics forward Jeff Green hit a hook shot with 3.3 seconds left.
Eight second-quarter turnovers shifted the game in favor of Boston, which was led by forward Gerald Wallace's 12 points off the bench.
Point guard Rajon Rondo, playing his first game since sustaining a knee injury last January, and Green both scored eight points for the Cletics, who shot 45.5% from the field.
Boston turned the ball over just twice in the first half, once each quarter.
Guard Manny Harris scored four points in his debut with the Lakers, who shot 50% from the field.
Rajon Rondo made his season debut, going scoreless in five minutes against the Lakers.
The Celtics scored 23 points despite making only 34.6% of their shots from the field.
Pau Gasol had eight points, six rebounds and three assists in a strong first quarter for the Lakers, who shot 50% from the field and committed only one turnover.
Jeff Green led the Celtics with six points. Boston kept close to the Lakers by pounding the offensive glass, with a 4-1 advantage.
Recently signed Manny Harris didn't score in almost six minutes of play.
The Lakers (14-25) play their second game of a seven-game road trip, visiting the Boston Celtics (14-26) at TD Garden on Friday night.
Rajon Rondo is expected to make his return after sitting out almost a year with a knee injury.
The Lakers have a long list of players out of action: Kobe Bryant (knee), Steve Nash (back), Steve Blake (elbow), Jordan Farmar (hamstring) and Xavier Henry (knee). They will also be without swingman Nick Young, who is suspended for throwing a punch in a game Wednesday against the Phoenix Suns.
Newcomer Manny Harris, freshly signed by the Lakers from the NBA Development League, could make his debut.
For a more in-depth breakdown, check out Preview: Lakers vs. Boston Celtics.