"I tried to be more aggressive from the beginning," said Bargnani, who matched a career high by going 5-of-10 from 3-point range.
The Raptors still had their 103-99 defeat from Friday night on their minds.
"We were very angry after (Friday's) loss," Bargnani said. "It was a bad loss."
Anthony Parker added 16 points and T.J. Ford came off the bench to score 15 as Toronto gave coach Sam Mitchell a victory in his 300th game. Mitchell is 137-163 as coach of the Raptors.
"Andrea was huge for us," Mitchell said. "He played great, he was just so consistent shooting the basketball."
The 7-foot Bargnani created all sorts of matchup problems for the hapless Knicks.
"That's tough," New York guard Jamal Crawford said of Bargani's outside prowess. "That's not something that you see. He's probably the only guy in the league with that range to be that big. He got it going tonight and that set the tone for them."
Crawford, who scored 43 points Friday, finished with 26 in this one, including 16 in the first half. Nate Robinson added 20 for New York, which has lost 11 of 14.
The Knicks have lost seven in a row in Toronto since a 109-103 win on March 5, 2004.
New York led twice, but never by more than a point, and went behind to stay midway through the first when a running dunk by Bosh gave Toronto a 13-12 edge.
Toronto led 54-52 at the half but blew the game open with an 18-3 run to begin the third.
Bargnani's strong start was all the more important for Toronto after Bosh went to the bench eight minutes in after picking up two quick fouls. Bosh returned for the third, but it was Toronto's shooters who were responsible for building the cushion.
Jose Calderon had two 3-pointers and Bargnani and Parker each made 3s before Bosh capped the run with a fadeaway jumper.
"The first four to five minutes of the third quarter, they came out and shot the ball well and they really knocked us out," Knicks coach Isiah Thomas said.
Bosh said Bargnani is more effective when he gets good looks early.
"We have to start him off the right way," Bosh said. "If he starts off the game with his feet set and he has time to make a decision and he's stepping into that 3, it's a little bit easier than falling away. That gives him a little momentum going into the rest of the game."
New York's Eddy Curry had 12 points and five rebounds in 26 minutes, the most he has logged in the past six games.
"It feels good to be out there," Curry said. "Right now, I'm just trying to find my rhythm. I'm a little bit out of sync. I've just got to go in early to practice, put up some shots and really stay focussed and try to make it as close to gamelike as possible so I can be ready when I'm called upon."
Knicks forward Zach Randolph went 2-for-13 and scored seven points.
"It's frustrating," Randolph said. "I couldn't buy a shot today."
Toronto center Primoz Brezec, acquired from Detroit on Thursday, made his Raptors debut in the second and finished with 11 points in 12 minutes.
"He surprised me with his intensity," Bosh said. "I'm liking what I'm seeing from him."