Randolph and Cousins figure to bang bodies when the visiting Grizzlies go for a fifth consecutive win over the Kings on Sunday.
After suffering its first set of back-to-back losses, Memphis (4-5) opened a four-game road trip with Friday's 89-86 win over the Los Angeles Lakers. Randolph, who was held to a combined 22 points in the previous two games, bounced back with 28 and 11 rebounds for his team-leading fifth double-double.
Marc Gasol also came up big with 18 points, eight rebounds, eight assists, three blocks and three steals.
"Everybody knows that we go as Zach goes. That's our horse, him and Marc. And we need them to continue that throughout the year," guard Tony Allen said. "Everybody came here with their antennas up, and everybody just wanted to get this win more than the other team. And it showed. We played hard for 48 minutes."
The Grizzlies improved to 4-1 when Randolph scores at least 15 points.
"Zach is Zach," Lakers coach Mike D'Antoni said. "You can try to stop it (but) you're not going to do it."
The Grizzlies, who had dropped their first three road games, held a 51-40 edge on the glass and outscored the Lakers 44-36 in the paint.
"It felt good, especially being our first road win of the season," Randolph said. "We had been up and down and inconsistent, so it was just good to get a win and build from here."
Randolph and company could be in for a stiff test down low against Cousins, who leads the Kings (2-6) with 22.8 points - 6.3 more than his career mark - and 10.0 boards per game. Cousins scored 26 on 12-of-23 shooting to go along with 13 boards and three blocks Friday, but Sacramento couldn't keep up with Detroit in a 97-90 defeat.
"DeMarcus Cousins is a heck of a player," Pistons center Andre Drummond said. "I knew what I was getting myself into tonight. He's one of the best centers in the league."
Isaiah Thomas added 18 points and seven assists off the bench and former Grizzlies guard Greivis Vasquez had 13 and six, respectively. However, Vasquez matched a career high with eight of the team's 17 turnovers.
"You can't win games if you consistently beat yourself," said coach Michael Malone, whose team has committed an NBA-low 102 turnovers. "This is one of the few games this year that we turned the ball over at a high rate.
While Kings fans set a Guinness world record for loudest noise at an indoor arena at 126.0 decibels Friday, Sacramento hasn't had much of a home-court advantage. The Kings are 1-4 on their own court this month.
Sacramento has dropped 11 of 13 to the Grizzlies, including all four matchups last season by an average of 14.3 points. Gasol has averaged 19.0 points, 10.7 boards and 3.0 blocks in the last three showdowns, while Mike Conley scored a combined 47 on 57.7 percent shooting in the last two.
Conley, averaging a team-leading 19.1 points, has posted just 11 in each of Memphis' last two road games while going a combined 8 of 26 from the floor.
Cousins has scored 22 or 23 points in four of his last five games against the Grizzlies.