With James tallying 29 points and Anthony Davis making 32 points and 13 rebounds, the Western Conference-leading Lakers beat the third-placed team in the East 114-112, recording a fifth straight victory.
In a frantic final quarter in LA after scores were tied at the last break, James had a chance to tie the scores with a free throw in the last minute but missed.
Seconds later, however, he atoned with his game-sealing fall-away jump shot to pen the latest chapter in the great Lakers-Celtics rivalry, whose most recent instalment was a stunning 32-point home win for the Celtics last month.
Jason Tatum matched his career-high with 41 points for the Celtics, who had won 12 of 14 before Sunday.
The Denver Nuggets stayed five-and-a-half games behind the Lakers in second place with a 128-116 win over the visiting Minnesota Timberwolves.
Paul Millsap made his first six shots of the game on his way to a season-high 25 points while Nikola Jokic poured in 24 for the Nuggets, who led at every break, including by 10 points at three-quarter time.
Kelan Martin had a career-best 21 points for lowly-ranked Minnesota, including 19 in the first half.
Kyle Lowry had 16 points and 11 assists to help the surging Toronto Raptors to their 17th win in 18 games with the biggest margin in their 25-year history – a 46-point thrashing of the Indiana Pacers.
The defending champions – second in the East to the Pacers' sixth – produced arguably the most comprehensive display of their red-hot past few weeks in winning 127-81, having led 34-12 at quarter time.
In a strong all-round display, six Toronto players had double-figure points totals, with Pascal Siakam making 21 and Serge Ibaka finishing with 15 alongside 15 rebounds.
Domantas Sabonis had 14 points and 11 rebounds for Indiana.
Elsewhere, the Chicago Bulls beat the visiting Washington Wizards 126-117, the Oklahoma Thunder won 131-103 at home to the San Antonio Spurs, the New Orleans Pelicans were victorious 115-101 at the Golden State Warriors, and the Portland Trail Blazers hung edged a 107-104 home win against the Detroit Pistons.