The starting forward scored 42 points in a 106-104 win, including the game-winning lay-up and free throw with 12 seconds remaining, and matched the franchise record with nine three-pointers.
Atlantic Division rivals the Boston Celtics were also victorious, but only after two periods of overtime against the Miami Heat - their second double-overtime game in succession.
Stand-out performer Paul Pierce, who had 17 points, 13 defensive rebounds and 10 assists, scored the winning points in a 100-98 win, Boston's first in seven games.
But the result was overshadowed by confirmation that guard Rajon Rondo will miss the remainder of the season after tearing his anterior cruciate ligament in Friday's defeat to Atlanta.
Pacific Division leaders the Los Angeles Clippers returned to winning ways for the first time in five games with a 96-83 success against the Portland Trail Blazers.
Blake Griffin had 23 points and nine assists for the Clippers, who have the third best record in the NBA despite their recent dip.
City rivals the Lakers toppled the Oklahoma City Thunder 105-96 in a tremendous game at the Staples Center. Kobe Bryant led their scorers with 21 points but his performance was more notable for his 14 assists, which tied his season's best set just two nights ago.
Both Bryant and Oklahoma's Russell Westbrook came up one rebound shy of a triple double, Westbrook with 17 points and 13 assists while Kevin Durant poured in 35 points.
Divisional rivals the Phoenix Suns went down 110-95 to the Dallas Mavericks, whose fellow South-West Division strugglers the New Orleans Hornets also won, 91-83 against the Memphis Grizzlies.
The Detroit Pistons beat the Orlando Magic 104-102, Brandon Knight and JJ Redick each scoring 31 points for the respective teams.