SACRAMENTO, Calif. -- DeMarcus Cousins missed Friday night's game with an illness, but he recovered quickly. Then he made the Knicks sick.

The Knicks erased a 14-point fourth-quarter deficit and pushed Saturday night's game into overtime, but Cousins spoiled their hopes of winning for the second time in 18 games.

Cousins had a monster game, finishing with 39 points and 11 rebounds to lead the Sacramento Kings to a 135-129 overtime win over the Knicks in the opener of a three-game trip. The Knicks lost their seventh straight game and fell to 5-27.

Carmelo Anthony tried to will the Knicks to the win. He had 36 points, 11 rebounds and six assists -- and he had help, for a change.

Tim Hardaway Jr. scored 19 points, including a driving layup that tied the score at 117 with 20.2 seconds left in the fourth quarter, and starting center Cole Aldrich scored 18 points, shot 8-for-9 and had seven rebounds before fouling out early in overtime.

But Cousins proved to be too much, scoring 20 of his points in the fourth quarter and overtime. Rudy Gay added 29 points and Darren Collison had 27 points and 10 assists for the Kings.

The Knicks had only nine players, so they may not have much left in the tank when they face the Trail Blazers (24-7) on Sunday night in Portland.

Amar'e Stoudemire, J.R. Smith, Andrea Bargnani, Iman Shumpert and Cleanthony Early all sat out with injuries. Quincy Acy served his one-game suspension for his flagrant foul 2 against John Wall on Christmas Day.

Stoudemire's health has become a concern. He has soreness in his right knee that could sideline him for all three games on this trip. Stoudemire has a history of knee trouble and has had his right knee scoped multiple times. He said he might undergo tests when the Knicks return home next week to see if it's more than soreness.

The Knicks, who fell behind 38-23 in the first quarter and 99-85 with 8:50 remaining in the fourth quarter, took their first lead of the game with 2:55 left in overtime when Shane Larkin's steal and layup made it 124-122. They took their last lead at 126-124 on Jose Calderon pull-up jump shot with 2:16 remaining.

After Cousins tied it with two free throws and Calderon missed twice on the next possession, Cousins fed Collison for a three-pointer that put the Kings up 129-126 with 1:22 to go. After the Knicks misfired again, Cousins drove baseline around two Knicks and threw down a ferocious dunk with 52.6 seconds to go to make it 131-126. The Kings extended the lead to nine before Hardaway hit a three-pointer with 4.6 seconds to play.

In regulation, the Knicks went on a 17-6 run and drew within 105-102 with 4:31 left on Hardaway's two free throws.

Cousins' follow made it 111-102 with 2:56 left, but Hardaway and Anthony connected on three-pointers on the Knicks' next two trips. Cousins then hit two straight jump shots to give the Kings a 115-108 lead with 1:45 to go.

Aldrich's hook shot made it 115-112 with 1:02 left, but Cousins made two free throws with 45.6 seconds left for a five-pointlead.

Anthony missed inside and couldn't convert the follow, but Aldrich got the rebound and was fouled as he went up. Cousins blocked his shot, but the officials reviewed it and called goaltending on Cousins. Aldrich completed the three-point play to make it 117-115 with 38.3 seconds to go.

Larkin's steal led to Hardaway's tying fast-break layup with 20.2 seconds left. Anthony forced a turnover, giving the Knicks a final shot in regulation with one second left. But out of a timeout, Gay blocked Anthony's three-point try to send the game to overtime.