Ersan Ilyasova added 16 points and a season-high 14 rebounds, and Luc Richard Mbah a Moute scored a season-high 17 points in his first start of the season for Milwaukee (11-9), which has its best 20-game start since 2005-06.
The Bucks never trailed and used a 12-2 run bridging the third and fourth quarters to take a 79-64 lead and put the game away.
Both teams were short-handed. Besides Cousins, the team's leading scorer and rebounder, the Kings were without key reserve forward Marcus Thornton (personal reasons). The Bucks were missing their two starting forwards, Larry Sanders (illness) and Epke Udoh (left wrist sprain), and key reserves Mike Dunleavy (bruised left knee) and Beno Udrih (right ankle sprain).
The offenses struggled as the Bucks shot 41 percent (39 for 96) from the field to Sacramento's 37 percent (32 for 86), and the Kings were just 3-of-19 (16 percent) on 3s.
The missed shots led to a lot of rebounds and Milwaukee finished with a 60-50 edge. Drew Gooden finished with 10 boards in his first extended playing time (22 1/2 minutes) of the season. He was inactive much of the year before making his debut last Friday.
Jason Thompson had a season-high 15 rebounds for Sacramento.
The Bucks jumped to an early 20-10 lead and led 29-19 after the first quarter, as Ellis sank a half-court shot to beat the buzzer. Sacramento used a 10-0 run to tie it at 32.
Two Bucks players picked up technical fouls with 2:04 left in the second quarter after exchanging words with referee Ken Mauer. Tobias Harris was whistled after arguing over a no-call following a layup attempt.
Then, as Harris was getting taped up near the bench, Mauer whistled Gooden, who was sitting on the bench. The technical free throws made it 43-39, but Milwaukee scored the last six points of the half to lead by 10 at the break. Mbah a Moute had 13 in the half.
Ellis added eight rebounds in his bid for his third career triple double.
NOTES: Milwaukee started 12-8 in 2005-06 en route to a 40-42 season. . Dunleavy has missed four straight games, and Udrih has missed six straight. . The teams' last meeting came on Jan. 5, when the Kings came from a 21-point halftime deficit to beat Milwaukee 103-100 in Keith Smart's coaching debut.