Foye made 8 of 13 shots, including 5 of 9 from the 3-point line, to lead Utah.
The Jazz played without starting point guard Mo Williams, who missed his third straight game with a severely sprained right thumb.
Foye "had a big game," said teammate Jamaal Tinsley. "He made tough shots. He was aggressive. That's what we need with Mo not here. So Randy needs to pick up the scoring and that's what he did tonight."
Said Paul Millsap: "He did great. He came out and was aggressive and kept us in the basketball game."
On Dec. 3, Foye scored 19 points on 7-of-11 shooting in a 105-104 loss to the Clippers.
His two-game totals against L.A.: 47 points on 15-of-24 shooting.
Lately, however, Foye has struggled.
In the Jazz's three previous games, he scored a total of 20 points and missed 20 of his 27 field-goal attempts.
"I needed a good night," Foye said.
Asked what changed for him, he said, "I just stayed aggressive. I haven't been shooting the ball as well as I wanted to. So I just got back in the gym and worked on it extra hard."
Foye was involved in two huge plays down the stretch.
After the Clippers took a 113-110 lead, he got to the basket, where he was fouled by DeAndre Jordan.
Foye made both free throws with 17.1 seconds remaining to keep Utah close.
"I just attacked, you know," Foye said. "[Matt Barnes] was playing up into my chest because he thought I was going to shoot it. He kind of jumped up on me. So I drove past him."
After L.A. took its 116-114 lead, the Jazz inbounded to Foye, who missed a 3-point shot after contact with Barnes.
"The second play ... maybe I should have just put my head down and drove again and tried to dunk the ball," Foye said.
The Jazz believed he was fouled.
"Tough situation," said Millsap. "They either call it or they don't. We felt like he got fouled but they didn't call it, so it just didn't happen."
Said Tinsley: "He was open. I passed him the ball. He took a shot. It is what it is."