Jessica Davenport added 13 points for the Liberty (12-16), who avenged a home loss to the Comets on July 20 and won away from Madison Square Garden for the first time since July 6 at Detroit.
Tina Thompson scored a game-high 24 points and Hamchetou Maiga-Ba added 16 for the Comets (10-19), who missed a chance to pick up a game in the standings against the Seattle Storm. The Storm lost at Minnesota on Tuesday.
Houston trails the Storm by 3 1/2 games for the fourth and final playoff spot in the Western Conference.
The Comets used a 6-2 run in the middle of the fourth quarter to get within 60-57 with 6 minutes to go, but the Liberty responded with an 8-2 run of their own to push the lead to 68-61 with just 3:25 left.
Davenport scored four points during that run and McCarville, who led New York with eight rebounds, made an easy layup for the seven-point lead.
The Liberty blew an eight-point lead in the second quarter before recovering to take a 39-37 lead at halftime.
Davenport hit a 12-foot jumper to give New York a 30-22 lead with 7:39 left before the Comets rallied with an 11-1 run to take their first lead of the game.
Michelle Snow started the rally with a short jumper and Thompson gave the Comets a 33-31 lead with a pair of free throws with 2:47 to go in the first half.
But the Liberty, who made seven 3-pointers in the first half, made two in the final 2:30 of the first half to regain the lead before the break.