Davis, the No. 1 overall pick in the draft, left with 4:51 to play in the first half after taking an inadvertent elbow to the temple from fellow rookie and teammate Austin Rivers. Davis had eight points - all on dunks - six rebounds and two blocked shots.
Vasquez, who had 13 points and 10 assists, drove past Gordon Hayward, who fell to the floor, and banked in a short shot over Al Jefferson. Utah had a chance to win after calling a 20-second timeout, but Mo Williams' fallaway 3-pointer at the buzzer bounced off the rim.
Robin Lopez and Ryan Anderson both had 19 points for the Hornets. Anderson's fifth 3-pointer with 32.7 seconds left gave them an 84-83 lead. After two free throws extended the lead to 86-83, Utah's Paul Millsap drained a 3-pointer to tie it and set up Vasquez' finish.
Reserve Randy Foye had 20 points for Utah while Williams added 16.
Utah shot just 41 percent from the field, but made ten 3-pointers.
The Jazz next play at San Antonio Saturday night.