Houston, holding the eighth and last Western Conference playoff spot at 30-26, also received forwards Francisco Garcia and Tyler Honeycutt from Sacramento in return for forward Patrick Patterson, center Cole Aldrich and guard Toney Douglas in a trade on Wednesday night.
The deal caught Houston players off guard as they were preparing to host last year's conference champion Oklahoma City Thunder.
Patterson, Aldrich and Douglas left the arena just as the game got underway.
"It was definitely the weirdest game I've ever played in," said Houston forward Chandler Parsons. "It was hard to focus."
The short-handed Rockets rallied from 14 points down to beat the Thunder 122-119 as former Oklahoma City guard James Harden poured in a career-high 46 points.
Houston took a gamble on the potential of Robinson, who so far had been a disappointment with the Kings (19-36). The 6-foot-10 (2.08 m) Robinson was averaging only 4.8 points and 4.7 rebounds in 16 minutes per game.
Patterson was the biggest piece given up by Houston. He had started 38 games this season and was the Houston's fourth-leading scorer, averaging 11.6 points.