In the end, the Clippers' poor shooting and inability to get timely shops did them in during a 110-103 loss to the Kings at Staples Center.
The Clippers shot only 39.6% from the field, 33.3% from three-point range in suffering their first defeat since a 100-99 setback against Oklahoma City on Dec. 21.
But Chris Paul struggled with his shot despite scoring 15 points and handing out seven assists. Paul was four for 11 from the field.
Sacramento's Rajon Rondo was three rebounds short of a triple-double, producing 13 points, 10 assists and seven rebounds.
DeMarcus Cousins led the Kings with 19 points and 13 rebounds.
The Clippers kept fighting to get up the hill in the fourth quarter after they got down 102-95.
Aldrich scored on back-to-back baskets to pull the Clippers to within three points. But Rondo scored to give the Kings a 104-99 lead with 1:13 left.
Paul made two free throws with 1:01 left and the Clippers were back to within three points, knowing they needed a defensive stop.
The Clippers got it when Rondo turned the ball over, but Paul Pierce missed a potential tying three-pointer, putting the Clippers in a position where they had to foul.
When they sent Rudy Gay (18 points) to the line, he made the first of two free throws for a 105-101 Kings lead.
Aldrich got the rebound of Gay's second missed free throw, allowing the Clippers to call a timeout with 15.6 seconds left.
They scored quickly when Pierce found Aldrich wide open for a dunk to pull the Clippers to within 105-103 with 13.1 seconds left.
But after Darren Collison (17 points) and Rondo made four consecutive free throws, the Clippers knew their winning streak was over.
The Clippers were down 64-60 at the half, then shot 26.9% from the field in the third quarter, making only two of 11 three-point attempts.
Paul continued to struggle in the third, missing five of his six shots. Luc Mbah a Moute missed all three of his shots.
That was the kind of shooting night the Clippers were having.
Not only did Blake Griffin miss his 10th consecutive game with a partially torn left quad, center DeAndre Jordan missed his second consecutive game recovering from pneumonia.
“He's not in the hospital so clearly he's getting closer and better,” Clippers Coach Doc Rivers said.
Their absence meant the Clippers' reserves had to step up again.
But then the Kings took control, primarily capitalizing on accurate shooting from long distance. Sacramento made 13 of 25 three-pointers for the game, with Omri Casspi connecting on five of eight on the way to 17 points off the bench.
Follow Broderick Turner on Twitter @BA_Turner