Jackson, a former Atlanta player, scored 32 points, including the winning shot over Maurice Evans and Al Horford. Jackson hopped onto the scorer's table before running off the court yelling, "That's what I do!"
Shaun Livingston scored a season-high 22 points as Charlotte earned its first win in Atlanta since 2007. Gerald Wallace had 16 points and 13 rebounds for the Bobcats.
Josh Smith had 28 points for Atlanta, which led by 22 in the second quarter and 18 in the third period.
The Hawks were 1 for 17 from the field in the first 9 minutes of the final quarter before Smith's left-handed jam and free throw tied it at 82.
Jackson's jumper gave Charlotte an 86-84 lead with 1:04 remaining. Horford's drive tied the game and, following a miss by Livingston, Atlanta called timeout with 23.8 seconds remaining. Joe Johnson missed a jumper, and the Bobcats controlled the rebound and called a timeout with 5.6 seconds remaining to set up Jackson's winner.
The Hawks led 70-52 in the third quarter before Charlotte regrouped with 14 straight points. The Bobcats' last lead was 7-6 in the opening minutes before taking a 75-74 lead early in the final period.
There were long runs in each of the first three periods. The Hawks had a 13-0 run in the opening period and then scored the first 18 points of the second period while building a big lead of 22 points.
The Bobcats, who missed their first 14 shots in the second period, recovered in the closing minutes of the first half and then rallied with a 14-0 run in the third period. Atlanta led 72-68 entering the final period.
Horford, the Hawks' All-Star center, had a double-double with 16 points and 10 rebounds after missing two games with a lower back contusion. He wore a brace on his lower back and needed to play through one period before gaining his confidence on offense.
Horford didn't attempt a shot while playing 7 minutes in the opening period, but he scored on an inside move to open the second quarter. Horford made his first five attempts, including four in the 18-0 run.
The Bobcats missed 10 straight shots in that span. Charlotte coach Paul Silas called two timeouts during the run, which ended when D.J. Augustin made two free throws with 5:31 remaining in the period.
The Bobcats' shooting woes continued until Jackson's layup with 2:26 remaining in the period ended the team's 0-for-14 drought.
Charlotte, while trailed by 22 at 51-29, scored 10 points in the final 2:26 of the period to cut the halftime deficit to 52-39.
Wallace made three 3-pointers early in the third period, and the Bobcats cut Atlanta's lead to 70-66 with a 14-0 run later in the period. Horford's jump-hook ended the run.
Notes: Charlotte ended a seven-game losing streak in Atlanta with its first win at Philips Arena since Jan. 19, 2007. ... Johnson and Mike Bibby each had 11 points while combining to make only eight of 24 shots.