In doing so, the Lakers hurt their own odds at the bottom of the standings, heading into the 2014 NBA draft lottery in May.
At 24 wins, the Lakers are sixth in the lottery standings, just one win "ahead" of the seventh-slotted Sacramento Kings (25-45).
The Lakers exploded for a franchise-record 51 points in the third quarter, scoring 4.25 points a minute.
Xavier Henry led the Lakers with 22 points off the bench, shooting 8-of-11 from the field. The Lakers also got 20 points from reserve Nick Young (5-of-6 from three-point range) and 18 from Kent Bazemore.
Kendall Marshall dished nine assists with just one turnover, along with seven points.
Carmelo Anthony led all scorers with 29 points, but the Knicks' bigger issue was easily on the defensive end.
The Lakers shot 57.8% from the field and 64.3% from three (18-28). New York hit 48.6% and 26.7%, respectively.
The Knicks travel to play the Sacramento Kings (25-45) on Wednesday night.
The Lakers were impressive in the second quarter with 36 points, but the third was an even greater onslaught as the team scored 51 to the Knicks' 31.
Ahead by as many as 30 points, the Lakers shot 60.9% from the field, 66.7% from three-point range and 90.0% from the free throw line.
The Lakers quickly made up their deficit to the Knicks in the second quarter, hitting nine of their first 10 shot attempts to climb ahead by 13.
Xavier Henry scored 13 in the period, hitting 5-of-7 including 3-of-4 from three-point range.
Kent Bazemore was also an offensive force, contributing 11 in the second while the Knicks got just six points from All-Star Carmelo Anthony in the half, on 2-of-10 shooting.
The Knicks shot 42.5% from the field while the Lakers improved from 27.8% in the first quarter to 52.6% for the game -- shooting 75% from the field in the second quarter.
The Lakers had 11 turnovers while the Knicks were also sloppy with nine.
It took a moment for the Lakers to get going on Tuesday night at Staples Center, falling behind 8-0 to the Knicks.
Once the Lakers got on the scoreboard, they got the next six to close within just two, but New York was able to push the lead back to eight by the end of the first quarter.
New York shot 39.1% from the field while the Lakers hit just 27.8% with five turnovers.
Neither Pau Gasol (vertigo) nor Steve Nash (nerve root irritation) is expected to play. Xavier Henry will play with a torn ligament in his wrist but the Lakers still don't have Kobe Bryant (knee) and Jordan Farmar (groin).
The Knicks are fighting to catch the 31-38 Atlanta Hawks for the eight playoff spot in the Eastern Conference.
For a more in-depth breakdown, check out Preview: Lakers vs. Knicks
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