Bryant finished with 31 points, 12 assists and 11 rebounds, while also becoming the first NBA player in history to record 30,000 points and 6,000 assists.
Kyle Lowry led the way for Toronto, which was playing its first game without DeMar DeRozan, with 29 points, nine assists and six rebounds. DeRozan is out indefinitely with a torn tendon in his left groin.
Terrence Ross had 20 points, while Greivis Vasquez and Lou Williams each added 19 points for the Raptors, who have lost two straight.
After Bryant and Lowry each made 1-of-2 from the foul line in the extra session, Wesley Johnson's 3-pointer rattled in and Bryant converted a three- point play to give the Lakers a 116-110 edge at 2:23.
Jonas Valanciunas answered at the other end with a dunk, but Bryant hit another jumper and Jeremy Lin got his layup to go after Ross was whistled for goaltending as the hosts stretched the margin to eight.
Ross made a 3 with 1:02 remaining in overtime to make it a two-possession game. However, the Lakers made their free throws down the stretch to hold on for the win.
Lowry's free throws with 2 1/2 minutes left in the fourth gave the Raptors a 103-102 lead. Jordan Hill followed by splitting a pair from the line, then Bryant converted a layup before driving the lane and kicking out to Nick Young, who buried a 3-pointer around a Valanciunas free throw for a 108-104 lead.
Lowry cut the deficit in half with two more free throws and he assisted on Ross' 3-ball that gave the Raptors a slim lead once again.
Bryant tied the game, however, on a free throw with 34.9 seconds left.
Lowry was called for an offensive foul after he hooked Ronnie Price on a drive to the basket, and Bryant lost the ball on the final possession of regulation when Valanciunas used the rule of verticality to stop him at the rim.
Williams scored eight straight points for Toronto, the last of which coming on three free throws for a 91-85 lead with under 9 1/2 minutes left in the fourth. Robert Sacre was fouled as he canned a tough turn-around layup and hit the free throw to tie the game at 95-95.
Bryant knocked down successive jumpers minutes later to push the Lakers in front by a 102-101 margin at 2:59 of the fourth.
Price's 3-pointer prior to the buzzer in the third gave the Lakers an 81-80 lead entering the fourth.
Bryant hit a jumper to close the first quarter and help Los Angeles to a 27-24 lead after 12 minutes. Young knocked down a 3-pointer to open the second and the Lakers never trailed in the quarter, taking a 58-49 lead into the break.
Hill had 16 points and 12 boards ... Patrick Patterson finished with 10 points and 13 rebounds in the setback ... There were 14 ties and 11 lead changes ... LA made 10-of-24 shots from beyond the arc, while Toronto made 9-of-34 shots from distance.