"There were some huge plays made and I'm so happy we got the win today because we needed this one, particularly with the losing streak we've been on," said Hayward, who was 10 of 17 from the floor and 3 of 6 from 3-point range.
No play was bigger than the 3-pointer Ingles nailed with 21.6 seconds remaining. That was the difference in the outcome.
"Joe (Johnson) set a great screen. Obviously, the play wasn't drawn up for me, but my guy hopped off, Joe screened his own guy and got me wide open," said Ingles, who hit 5 of 8 field goals overall and 3 of 6 on 3-pointers.
Ruby Gobert collected 12 points and 11 rebounds for the Jazz (19-13), which improved to 3-0 this season against the Lakers. Johnson and Boris Diaw chipped in 10 points each.
D'Angelo Russell, who made just 2 of 11 shots and missed all three of his 3-point attempts for four points, fired an air ball from behind the arc just before the final horn, allowing Utah to prevail.
"We wanted him to turn the corner and then there was an option for either him or Lou (Williams) coming off a screen," Lakers coach Luke Walton said. "We didn't get into it with the pace and space, and they switched some stuff and we got a little confused."
The teams exchanged leads down the stretch. Russell made a jumper to tie the score at 95, but Hayward converted two free throws for a 97-95 edge. However, the Lakers snatched the lead on consecutive buckets by Randle to go up 99-97 with 1:09 remaining.
Gobert scored inside to knot the score again at 99 with 56.5 seconds left.
After the Lakers committed a 24-second clock violation, Ingles' big shot boosted the Jazz to a 102-99 advantage.
Randle converted one of two foul shots with 14 seconds remaining to slice the margin to two, and the Lakers got a break when Gobert missed a pair of foul shots with 13.1 seconds left. But they failed to convert on their final possession.
"We didn't assume he was going to miss both at the free-throw line," Russell said. "We still had to play up and it came down to us not making the shot, and it was a tough one."
Utah's defense had something to do with that.
"I thought we started defending better in the second half, and there was a period where they hit some tough shots," Jazz coach Quin Snyder said. "Lou obviously. I've been watching him do that since we were in Philadelphia together. He's just got a knack."
Both clubs struggled offensively in the third quarter. The Jazz managed to make 40 percent of their shots to only 36.8 percent for the Lakers. However, the Lakers, who outscored the Jazz 24-22 in the quarter, held a 74-72 edge heading into the final period.
The Lakers led 52-48 at the break despite being outshot 51.3 percent to 46.8 percent. The Lakers also had trouble hitting 3-pointers, misfiring on 9 of 10 attempts while the Jazz made 5 of 16 (31.3 percent).
For the game, Utah shot 50.7 percent and the Lakers 47 percent.
The Jazz won despite committing 20 turnovers (leading to 24 points) to 16 (22 points) for the Lakers.
The game featured 18 lead changes and 13 ties.
NOTES: Jazz G George Hill (sprained left big toe) practiced Monday and participated in the team's shootaround Tuesday but did not play Tuesday night. Hill, who missed his 13th game, is close to returning, although coach Quin Snyder did not say when. ... Utah G Dante Exum (left knee tendinitis) missed his third contest. ... Los Angeles F Larry Nance (bone bruise, left knee) began rehabbing this week. Nance is expected to be sidelined the next four weeks. ... Lakers assistant coach Mark Madsen underwent an appendectomy and is out indefinitely. ... The teams meet for the final time during the regular season Jan. 26 at Utah. ... Both clubs resume play Thursday at home. The Jazz face the Philadelphia 76ers, while the Lakers play the Dallas Mavericks.