Jordan Hill gave the Lakers a chance with a strong performance in the fourth quarter, scoring 13 points, including a pair of free throws with 18.6 seconds left to tie the score at 103.
Lakers guard Jodie Meeks missed a long three-point attempt at the buzzer.
Lakers guard Nick Young fouled out with about 4 1/2 minutes left in the game after leading the Lakers with 21 points. The team played the game without Pau Gasol (upper respiratory infection), Kobe Bryant (knee), Steve Blake (elbow) and Steve Nash (back).
Hayward led all scorers with 24 points and he had nine assists. Favors had 18 points and 14 rebounds. Rookie point guard Trey Burke finished with 14 points and seven assists, but he also turned the ball over seven times.
The Lakers shot 50% from the field but only 30.4% from three-point range and 69.6% from the free-throw line.
The Jazz shot 45.5% from the field and 39.1% from three-point range. They also made 16 of 20 free throws and outrebounded the Lakers, 43-37.
The Lakers fall to 13-17. They'll return home to host the Philadelphia 76ers (8-20) on Sunday.
The Jazz (9-23) will visit the Clippers on Saturday.
After the Jazz pushed ahead by as many as eight points, Nick Young came off the bench to score 13 in the quarter to get the Lakers to within two heading into the fourth.
Utah shot 46.5% from the field, 50% from three-point range and 90% from the free-throw line. The Lakers hit 52.5% from the field but struggled at 30% from long range and 64.7% at the line.
Trey Burke scored seven consecutive points to wipe out a four-point deficit to the Lakers and give the advantage back to the Jazz.
Burke shook off what appeared to be a sprained ankle in the first quarter to score 11 points for Utah. Derrick Favors led the Jazz with 12 points.
The Lakers shot 48.7% from the field but missed six of 17 free throws. The Jazz shot 46.9% from the field and 83.3% from the free-throw line.
In 9 1/2 minutes against Utah, Kaman scored eight points, had five rebounds and blocked two shots.
The Lakers shot 50% from the field and the Jazz just 40.7% from the field, yet Utah was able to take a two-point lead heading into the second quarter.
Jordan Farmar contributed seven points and three assists for the Lakers.
The Lakers (13-16) will visit the Utah Jazz (8-23) on Friday night, hoping to break a three-game losing streak.
The Jazz are in last place in the Western Conference and only won three of 13 games at home, giving the Lakers an opportunity to start edging back to .500.
Pau Gasol will miss the game with an upper respiratory infection. Chris Kaman is expected to start at center.
For a more in-depth breakdown, check out Preview: Lakers vs. Utah Jazz.