Trevor Ariza added a career-high 21 points and shot 8-10 from the field, which included going 3-4 from three-point land. Pau Gasol had 20 points and nine rebounds for the Lakers.
Statistically, Utah performed well. They out-rebounded the Lakers (46-38) and had more assists (28-22), while also committing few turnovers (14-17).
It all counted for little however, as Utah's shooting was woeful. The Jazz made only 39 percent of their field goals compared to a sizzling 56 percent by the Lakers.
Utah was also unable to capitalize on a strong effort on the offensive glass, where they collected 20 of their 46 rebounds.
Utah point guard Deron Williams scored 16 points and handed out 17 assists, but he was one of the teams' worst performers shooting the ball, making just 4-14 from the field and only one field goal after the first quarter.
Carlos Boozer added 27 points and grabbed nine rebounds for the Jazz.
The Jazz were without the teams' second-leading scorer, Mehmet Okur, who missed the game with a sore right hamstring.
Early on, Bryant deferred to his teammates and Ariza and little-used backup point guard Shannon Brown. Brown was called into action after Derek Fisher was whistled for two quick fouls.
Both Ariza and Brown hit two three-pointers in the first quarter as the Lakers built an early lead.
Los Angeles continued to dominate in the second period and by halftime, the lead had blown out to 22 points, 62-40.
The Jazz opened the second half on a 9-0 run to close the gap, but after Bryant was called for a technical foul, the Lakers regained control and a three-point play by Trevor Ariza and extended the lead back to 16 points, 70-54.
Utah continued to chip away at the Lakers' lead and when Andrei Kirilenko connected on a three-pointer with 5:44 left, the Jazz had cut the lead back to nine points, 98-89.
However, Bryant immediately responded for the Lakers and made consecutive jump shots to take the lead back to 13 points.
The Jazz continued to push and again closed to within nine points with just under two minutes to go, before Bryant again answered, this time with a thunderous one-handed dunk on which he was fouled on by Paul Millsap. Bryant made the free throw to convert the three-point play to effectively seal the win for the Lakers.
Things don't bode well for the Jazz for the rest of the series, considering that head coach Jerry Sloan said prior to the series that his teams' chances of defeating the Lakers were "pretty bleak".
Game two is Tuesday in Los Angeles.