Andrea Bargnani had 28 points and 10 rebounds on Sunday to help Toronto beat New York 111-100 two days after absorbing a 30-point loss against the Knicks.
"We wanted to come out and set a different tone from the beginning and just let them know that this isn't going to be that kind of night," said Parker, who finished with 24 points.
Each of Toronto's starters reached double figures and four of the five had double-doubles. Shawn Marion had 16 points and 15 rebounds, and Chris Bosh added 11 points and 12 boards. Jose Calderon had 13 points and 11 assists.
"It's good the way this team responded to adversity," Bosh said. "It's all about effort. We played good defense, we rebounded the ball well and, for the first time in a very long time, we ran the fast break well."
The Raptors added the athletic Marion in a Feb. 13 trade with Miami and hope to make running a priority for the remainder of the season.
"When you're able to do that the game comes naturally, it starts feeling better," Marion said. "That's when you start feeling the rhythm and everything starts coming together."
Al Harrington scored 31 points and David Lee had 17 points and 15 rebounds for the Knicks, who have lost nine straight games in Toronto and 11 of 12 overall against the Raptors. Chris Duhon finished with 17 points.
"They played a lot harder," Harrington said. "They were a lot more focused. They were determined to win this basketball game."
Nate Robinson scored 12 in the fourth quarter and finished with 18. His layup with 3 seconds left gave New York 100 points for the 16th straight game.
The Knicks beat Toronto 127-97 in New York on Friday night behind a career-high 32 points from Wilson Chandler, who was ineffective in the second half of the home-and-home. He went 1-for-6 from the field and scored two points in 21 minutes.
Toronto led 82-74 after three quarters and pushed its lead to 92-82 when Bosh completed a three-point play with 8:21 remaining.
A three-point play by Harrington and a layup from Robinson made it 104-98 with 2:31 left, but Bargnani answered with a 3-pointer.
Knicks coach Mike D'Antoni said his team's defense "wasn't firing on all cylinders" in the second half.
"I was just a little disappointed in our getting back on defense," he said. "Maybe we were surprised by them but we lost the theme of the game right in the middle of the third quarter."
Larry Hughes and Chris Wilcox, acquired in separate deadline-day trades last week, made their Knicks debuts. Hughes struggled with his shooting, going 1-for-9 for three points, and Wilcox scored five.
Hughes, who hadn't played since Jan. 12, acknowledged his timing was off, but said he felt comfortable in the Knicks' system.
"When you haven't been playing it's kind of tough," Hughes said. "I felt like I was understanding what we wanted to do. It's just a matter of executing."
With Hughes and Wilcox in the mix, D'Antoni may struggle to find enough minutes for all of his players. First-round draft pick Danilo Gallinari, whom D'Antoni warned before the game would be used sparingly, if at all, did not play for the first time since a Jan. 24 loss at Philadelphia.
"It's fine to me, I don't have a problem," Gallinari said.
The teams were tied at 27 after the first and Toronto began the second with a 12-0 run, including back-to-back 3-pointers from Roko Ukic and Jason Kapono. New York recovered, and Harrington's 3-pointer with 5:02 left in the half tied it at 46. Toronto led 57-53 at the half.
New York's last win in Toronto was a 109-103 victory on March 5, 2004. ... New York is 7-20 on the road. ... The last time four Raptors had double-doubles was Feb. 23, 2001, when Vince Carter, Antonio Davis, Charles Oakley and Alvin Williams did it in a triple-overtime victory over Sacramento. ... Toronto guard Marcus Banks (back spasms) did not dress. ... The Raptors celebrated the 10th anniversary of the Air Canada Centre. Toronto beat the Vancouver Grizzlies 102-87 in the arena's first basketball game on Feb. 21, 1999.