And for the second time this season, they benefited from a late technical foul on New York's Al Harrington after a dunk that had given the Knicks a three-point lead in the final half-minute of regulation.
Harrington finished with 38 points for the Knicks, who matched a season high with their sixth straight loss.
New York raced to a 19-point lead in the first 6:01, heard boos after blowing all of it before halftime, and ended up with another embarrassing loss against one of the NBA's worst teams as it limps to the finish of its eighth straight losing season. Wilson Chandler backed Harrington with 22 points.
The Knicks know Randolph well, having traded him to the Clippers in November in a deal that helped them clear salary-cap space for the summer of 2010 but weakened them for now. He was their leading scorer at the time and had helped New York get off to a promising start, fitting in better than expected under Mike D'Antoni.
Taylor is much less known, coming into the game averaging 3.9 points in his rookie season. Yet he was so good Clippers coach Mike Dunleavy used him instead of the struggling Baron Davis to open the second half, and he played 37 minutes.
Neither team led by more than five in the second half and Harrington's driving dunk gave the Knicks a 127-124 lead with 27 seconds left. But he was called for hanging on the rim, and Gordon hit the technical free throw to make it a two-point game. Randolph tied it with two free throws with 13 seconds remaining, and Chandler was short on a potential winning 3-pointer.
The Knicks lost in overtime at Los Angeles last month after Harrington gave them a three-point lead on a dunk with 25 seconds left in regulation but was called for a tech for slapping the backboard.
Taylor knotted it with a jumper with 2½ minutes left in the extra period, Randolph followed with a bucket and Taylor banked in a runner in the lane for a 137-133 lead with 1:35 left.
The Clippers had lost three straight overall and averaged only 76.5 points in the last two. They passed that less than 4 minutes into the second half against a Knicks team that recently absorbed home losses against sub.-500 teams New Jersey and Sacramento by a combined 53 points.
The Knicks made 13 of their first 15 shots and were up 27-8 after Chandler's jumper with still 5:59 remaining in the first quarter. New York led 44-28 after one, shooting 79 percent (19-of-24) in its best period of the season.
The Clippers wasted no time coming back behind Taylor, who became the first player drafted directly from the NBA Development League when Portland took him in the second round in 2008. His jumper capped a 13-2 spurt to open the second quarter and got Los Angeles within five.
Taylor scored 17 in the quarter - surpassing his previous career high of 15 for a game. He blew by the Knicks for a layup that gave the Clippers a 63-62 edge with 1:50 remaining, eliciting loud groans from the Madison Square Garden crowd, but the Knicks recovered for a 66-65 advantage at halftime.
The Knicks shot 64 percent in the first half and the Clippers made 59.5 percent of their attempts. They picked right up where they left off after the break, with Los Angeles hitting six of its first eight shots and New York starting 6-of-9. Thornton scored nine points as the Clippers brought a 95-93 lead into the final quarter.
Notes: D'Antoni said he hadn't spoken Wednesday with rookie forward Danilo Gallinari, who has returned from a trip home to Italy to get further opinions on his ailing back. Gallinari is considering surgery that would sideline him for the season. ... The Knicks had scored 43 points in a quarter twice this season.
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