The Bobcats led by as many as 10 in the fourth quarter, but the Raptors took the lead after a late run.
Sessions made a jumper from just beyond the foul line that hit the rim twice before falling through to give the Bobcats the lead. Toronto had four shots to win it, but two resulted in blocks and Andrea Bargnani's baseline jumper fell short as time expired.
Kemba Walker had 19 points and seven assists for the Bobcats, while Sessions and Michael Kidd-Gilchrist each had 14 points.
Bargnani had 25 points and Kyle Lowry added 21 for the Raptors. Jonas Valanciunas added 16 points and 10 rebounds.
The Bobcats improved to 5-0 in games decided by four points or fewer.
The Bobcats (6-4) are one win away from equaling last year's season win total. They were 7-59 last season.
Walker and Sessions continue to be an impressive tandem for the Bobcats as both have scored in double digits all 10 games this season.
The Bobcats got some quality minutes from second-year power forward Bismack Biyombo, who's not typically known for his offensive prowess.
Biyombo had six of his 11 points in the third quarter, including a powerful dunk over Bargnani after battling for control of an offensive rebound. He also had a key block on
Biyombo was 5 of 6 from the field and had five rebounds and was on the floor at the end of the game ahead of Byron Mullens because he was playing so well.
The Bobcats led by as many as 10 early in the fourth quarter before Jose Calderon hit a 3-pointer, DeMar DeRozan scored on a layup and jumper and Bargnani hit a jumper from the top of the key to tie the game at 88 with 4:50 to play. Bargnani then knocked down a 3-pointer to give Toronto the lead with 1:52 to play.
But the Bobcats kept battling with Walker driving the left side of the line and scoring and drawing a sixth foul on Valanciunas. Walker finished the 3-point play to tie the game with game with 55 seconds left.
DeRozan hit one of two free throws at the other end before Sessions got a foul line jumper to drop after hitting the rim three times giving Charlotte the 98-97 lead with 28.3 seconds left.
Toronto missed three shots at the other end and two of those were blocked.
The Raptors set up an inbounds play for Lowry with 6.4 seconds left and he got off a 12-footer that was blocked by rookie Jeffery Taylor.
Valanciunas had another shot as time expired but couldn't knock it down and the Bobcats held after a furious defensive stand.
The score was tied at halftime following a back-and-forth first half.
Lowry had 16 points at the break after hitting all three 3-point attempts for the Raptors, while Walker had 10 points for the Bobcats.
The Raptors were coming off a 106-98 loss at Philadelphia and Bobcats coach Mike Dunlap said before the game the goal was to pressure Toronto as much as possible and try to wear them down.