Anthony was in prolific form during the opening quarter when he fired 22 points as the hosts raced into a 41-27 lead.
They stretched this advantage to 68-49 by half-time en route to making it nine straight home wins.
But Anthony was unable to finish the contest after suffering a heavy fall half-way through the third quarter and left the arena never to return.
The Knicks have the best record in the Eastern Conference of the NBA and lead the Atlantic Division by a decent margin (17-5).
Kobe Bryant led the way for Los Angeles with 31 points, 10 rebounds and six assists.
However, the visitors slipped to a fourth successive loss and have now won just nine of their 23 matches this season.
The game marked a return to Madison Square Garden for Lakers coach Mike D'Antoni, who resigned as coach of the Knicks last March.