The Jazz (40-37) entered a half-game behind the Los Angeles Lakers for the final playoff spot in the Western Conference. The Lakers faced Memphis in a late game.
Utah led by just four entering the fourth but opened the quarter on an 8-0 run, capped by Hayward's 7-foot jumper. He scored 10 straight as Utah surged ahead 87-73 with 4:47 remaining.
The Hornets got no closer than 10 and scored just 16 in the fourth.
Derrick Favors added 10 points, 10 rebounds and a career-high six blocked shots for the Jazz.
Anthony Davis scored 24 and Greivis Vasquez added 21 for the Hornets (26-50), who lost the season series to Utah 3-1.
The Jazz hardly looked like a team in a playoff race early. The arena was half empty at the start of the game and the Jazz were cold, shooting 29.4 percent late in the first as New Orleans built an 18-11 lead.
The Hornets led 24-17 after one, outscoring Utah 16-8 in the paint and 8-0 on the break while holding a 12-7 rebounding edge.
The Jazz used a 23-8 run to start the second quarter, building a 40-32 lead.
Utah did it with an odd combination, with starter Paul Millsap playing alongside reserves Jamaal Tinsley, Alec Burks, Carroll and Favors. The unit had played just six minutes together before but they clicked Friday.
Tinsley, Carroll and Burks had 3-pointers early in the run, and Carroll kept it going by diving on the floor for a steal to set up Millsap for a short bank shot. Millsap converted a three-point play, passed inside to set up a dunk by Favors, then scored on a follow shot with 3:54 left in the half.
Millsap hit a 3-pointer as the shot clock expired for a 45-39 Utah lead before the Hornets pulled to 45-43 at the break.
Millsap started 5 of 5 and was 7 of 8 at halftime with four rebounds, four assists and a block. He finished 8 of 13, with 10 rebounds.
Carroll finished with three steals, three assists and three rebounds after subbing in for a cold Hayward.
Hayward had such a bad start Jazz coach Tyrone Corbin had to make the switch. Hayward was 1 of 6 (1 of 4 from 3-point range) and missed a pair of free throws before being replaced in the first quarter. He missed both attempts in the second quarter and was 1 of 8 at halftime for three points.
He scored 20 points in the second half as Utah took control.
The Jazz shot 50.6 percent and hit 11 of 26 3-pointers, with Hayward making 5 of 10.
New Orleans shot just 41.5 percent and 2 of 12 from 3-point range.
The Hornets won the battle in the paint, outscoring Utah 48-38.