Trailing 65-61, the Kings outscored the Magic 22-2 in the final 5:03 of the third quarter to take an 83-67 lead into the fourth. Sacramento led by as many as 16 points in the final period.
Orlando surged within 87-80 in the fourth, but after Even Fournier was called for a technical for arguing an offensive foul, the Kings got the lead back up to double digits.
Tobias Harris led the Magic with 24 points. Fournier added 17.
The Magic were 1 for 8 from the field with five turnovers during Sacramento's third-quarter spurt. Those five turnovers led to eight Kings points.
Cousins was back in the lineup Saturday after serving a one-game suspension for hitting Atlanta's Al Horford with a forearm to the head on Wednesday.
Cousins carried the offensive load for the Kings in the first half, scoring 15 points. Sacramento entered the night averaging nearly 104 points per game, but recovered from shooting just 37 percent from the field in the opening 24 minutes.
After being benched in the second half of the Magic's win over Minnesota on Wednesday, center Nik Vucevic started on Saturday and appeared more engaged on both ends of the floor.
He finished with 11 points and 11 rebounds, but again sat the entire fourth quarter as the Magic tried to get back into the game.
TIP-INS: The Kings were 28 of 31 from the free throw line. ... Sacramento's bench outscored the Magic's bench 36-21. ...Vucevic recorded his fourth double-double of the season. ...The Magic were called for three technical fouls, including one on coach Scott Skiles.
Kings: Visit Charlotte on Monday.
Magic: At Cavaliers on Monday.