The Hornets evened their record at 1-1, but the victory could have been a costly one with No. 1 draft choice Anthony Davis leaving the contest with an apparent concussion.
Davis suffered the injury with 4:51 remaining in the first half after he had scored eight points, grabbed six rebounds and blocked two shots. Davis had scored 21 points in his NBA debut on Wednesday.
The game was close throughout and the Jazz tied it with 9 seconds to go in the fourth quarter on a 3-pointer by Paul Millsap.
After taking a time out, New Orleans worked the ball to Vasquez and he came through with the winning drive and basket. Vasquez has opened the season as the Hornets' starting guard in his third season in the NBA.
Utah, which has also split its opening two games, was led by 20 points from Randy Foye.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys