The Jazz had lost their first eight games of the campaign, but rallied in the fourth quarter after trailing by as many as 16 points in the third.
Favors put Utah in front to stay at 98-97 with 3:18 to play by hitting a layup and he converted another one to put the Jazz in front by five with 27 seconds remaining.
Diante Garrett played his first game of the season with Utah after beginning the campaign in the NBA Developmental League. The point guard from Iowa State made an impact with seven points and five assists.
Anthony Davis had 29 points and 15 rebounds for the Pelicans, who have lost three in a row.