Bobcats coach Mike Dunlap called the defensive stand "two-thirds willpower and one-third technique."
"We were trying to switch everything, but at the end, coach said just stay with your man," Biyombo said. "We had to make quick decisions, and I think we made pretty quick decisions and we did a pretty good job as a team. It was just big time."
Kemba Walker had 19 points and seven assists for the Bobcats, while Sessions and Michael Kidd-Gilchrist each had 14 points. Walker and Sessions have both scored in double digits in all 10 games.
The Bobcats won despite shooting 42 percent from the field and 15 percent from the 3-point range.
"We won ugly tonight, but it doesn't really matter," Dunlap said.
The Bobcats got some quality minutes from Biyombo, who's not typically known for his offensive prowess. The second-year forward had six of his 11 points in the third quarter, including a powerful dunk over Bargnani after battling for control of an offensive rebound.
Along with his key block on Toronto's final possession, he was 5 of 6 from the field.
"He was excellent," Dunlap said. "He was all professional tonight. The rebounding, plugging the gaps. He did a lot of the dirty work tonight. I thought as a team we were a little flat, but he wasn't. In many ways he ignited us."
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 a 3-point 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 1-of-2 free throws at the other end before Sessions got a foul line jumper to drop with 28.3 seconds left.
After two misses, the Raptors set up an inbounds play for Lowry with 6.4 seconds left and his 12-footer was rejected by Taylor. Valanciunas had another shot as time expired but couldn't knock it down, and the Bobcats held after a furious defensive stand.
"These guys played their heart out and they are hurt right now," Raptors coach Dwane Casey said. "We have to create some breaks for ourselves. I thought we shot ourselves in the foot with some mental mistakes that we made as far as turnovers are concerned."
Lowry had 16 points at the break after hitting all three 3-point attempts for the Raptors.
"It's very frustrating. We're working so hard," Lowry said. "But we've got to get better. Our 3-9 record doesn't show how good of a team we are. We're better than 3-9."
The Bobcats had a streak of 29 straight free throws snapped when Biyombo missed in the second quarter. ... Bargnani's 25 points were his season high. ... Raptors guard Terrence Ross gave his team a boost off the bench with 11 points.