In the first quarter, Cousins took exception when Morris knocked Jae'Sean Tate to the floor. He shoved Morris back in response.
Morris initially received a flagrant-1 foul before being assessed a technical foul along with Cousins. Although Morris was ejected, Cousins remained in the game. He didn't stay for very long as he was sent to the locker room early in the second quarter for a hard foul on LeBron James.
Referencing the interaction between Cousins and Morris, Rockets head coach Stephen Silas supported his player.
"I thought [Cousins] was sticking up for his teammate on the first part, the first technical, and I'll support him 100 percent when he's sticking up for his teammate," Silas told reporters. "He was sticking up for Jae'Sean. He wasn't going to allow anything to happen to his rookie, and I think that's admirable."
Anthony Davis played down any continued friction between the two players, who share an L.A. connection since Cousins was waived to make way for Morris' arrival in the middle of last season.
The Rockets and Lakers cross paths again Tuesday, setting up a potential for further individual clashes.