James, who finished an assist shy of a triple-double with 13 rebounds and nine dishes, sunk the winning basket with less than a second less to play.
Stephen Curry led the Warriors with 29 points.
Blake Griffin poured in 36 points to lift the Los Angeles Clippers to a 122-117 victory over the Portland Trail Blazers.
Chris Paul backed up Griffin's effort with 20 points and 12 assists, while LaMarcus Aldridge paced the Blazers with 25 points.
Tim Duncan scored 25 points as the San Antonio Spurs overcame the Boston Celtics 104-92.
Marco Belinelli added 16 points, 11 rebounds and eight assists to support Duncan, who scored all but two of his points in the second half.
James Harden scored 35 points, including the winning lay-up with less than a second on the clock, as the Houston Rockets beat the Washington Wizards 113-112.
Kevin Love's 32 points and 11 rebounds helped the Minnesota Timberwolves to a 117-90 victory over the Denver Nuggets.
DeMar DeRozan poured in 31 points while Kyle Lowry added 16 points and 13 assists as the Toronto Raptors overcame the Atlanta Hawks 104-83.
Twenty-three points from Monta Ellis helped the Dallas Mavericks beat the Indiana Pacers 81-73, while Paul Pierce had 25 in the Brooklyn Nets' 105-89 win over the Charlotte Bobcats.
The Sacramento Kings beat the New York Knicks 106-101 in overtime, the Cleveland Cavaliers were 93-89 winners over the Detroit Pistons and the Memphis Grizzlies saw off the Orlando Magic 86-81.
There were also wins for the New Orleans Pelicans and the Utah Jazz.