It was the 1,000th triumph in Karl's career, making him the seventh NBA coach to reach that figure. The Nuggets had dropped their previous two attempts to bring Karl the historic win.
Harrington made six of Denver's 12 3-pointers and hit on 12-of-19 attempts from the field overall.
The Nuggets trailed by a point with 4:15 to play in the second quarter but closed the half on a 14-4 run and opened as much as a 19-point lead in the third period.
Nene contributed 26 points for Denver, Chauncey Billups had 21 and Gary Forbes scored 15.
Toronto, which has lost four straight, was led by Linas Kleiza with 26.
Both teams shot more than 50 percent and Denver survived 22 turnovers to pick up its eighth victory in 10 games. The Nuggets played without Carmelo Anthony (knee) for the second straight game.