"He didn't like it," coach Mike Woodson said, "but he bought in."
Smith received 484 points, including 72 first-place votes, from a panel of 121 writers and broadcasters. The Clippers' Jamal Crawford finished second with 352 points, getting 31 first-place votes.
"I just wanted to show everybody that I could be a team guy and it's all about the team," Smith said at a news conference attended by his family, teammates and coaches.
Smith averaged 18.1 points in 80 games, all off the bench. He had 29 games in which he scored 20 points as a reserve, tying Crawford for the NBA lead.
"Couldn't have happened to a better guy," said Woodson. "I'm so proud of him, in terms of buying in to what we wanted him to do earlier in the season. And it started this summer. I wasn't going to start him, coming into this year, and I knew that. And he bought in. He didn't like it, but he bought in. And it couldn't have happened to a better person, because he put in the time and he worked his butt off to get to this point, and he got rewarded for it. I'm happy for him."
Smith helped the Knicks win the Atlantic Division title for the first time since 1994. New York is the No. 2 seed in the Eastern Conference and leads the Boston Celtics 1-0 in their first-round playoff series.
It's the second individual award in two years for the Knicks, following Tyson Chandler's Defensive Player of the Year honor last season.
Smith is the third player in Knicks history to win the NBA's Sixth Man Award, joining John Starks (1996-97) and Anthony Mason (1994-95).
Despite not making a start, Smith was one of the Knicks' most important players. He played more than 40 minutes seven times and was often their only scoring threat behind Carmelo Anthony.
Anthony, who teamed with Smith for 4½ seasons in Denver, noted that Smith had a more mature approach to the game this year.
"I think there comes a point in time in your life where you're almost forced to grow up, you're almost forced to mature. You gotta be willing to want to do those things. I think right now, this season, J.R. has done that," Anthony said. "I think J.R. was forced to grow up, he was forced to be mature and he was willing to take on that challenge, too."
For most of the season, it seemed like Smith would take second place to Crawford.
He struggled for much of January, shooting 36 percent from the floor in that month, including just 25 percent from beyond the arc.
But during the Knicks' 13-game winning streak late in the regular season, the New Jersey native was a model of consistency. He scored 23.2 points per game on 49 percent shooting; prior to the winning streak, Smith averaged 16.7 points per game on 40 percent shooting.
Smith doubled the percentage of shots he took in the restricted area during the winning streak (15.6 percent before March 18; 33 percent in the 13 games following it).
"He went through a phase when he [was] just shooting jump shots and jump shots and finally a green light went off and he started taking the ball to the bucket," Woodson said.
Smith had three straight 30-point games March 26-29, the first time that was done by a reserve since Milwaukee's Ricky Pierce in 1990.
Crawford said he and Smith exchanged congratulatory texts.
"I can't say I was shocked because I started seeing where it was going over the last few weeks," said Crawford, who thinks he and Smith have different roles with their teams.
"He is the second guy over there after Carmelo," Crawford said. "I'm just a piece of the bench."
Earlier this season, Crawford was left off the NBA All-Star team in a move many across the league felt was a mistake. Now, despite leading what is considered among the top bench units in the league, Crawford is again left empty handed.
"I learned with the All-Star Game that you can only control what you can control," Crawford said. "Whenever it's up to the coaches or media or whatever, you expect the unexpected."
Smith ended the season leading all bench players in points per game (18.1). Crawford was second with 16.5 points per game. Golden State's Jarrett Jack finished third, followed by Kevin Martin of Oklahoma City and Ryan Anderson of New Orleans.
Smith came to the NBA out of high school in 2005 and admittedly made a number of mistakes along the way. He clashed with coaches and pleaded guilty to reckless driving in a 2007 auto accident that killed his friend, spending 24 days in a New Jersey correctional facility and getting suspended by the NBA for the first seven games of the 2009-10 season.
"I've been known to make so many mistakes I haven't been making recently," said Smith, thanking his veteran teammates and Woodson for helping him. "Just keeping my head, mentally on the court and off the court."
Smith signed a two-year contract worth $2.8 million in the offseason. The second year has a player option, and Smith is expected to decline it and test free agency.
The Knicks will have Smith's early Bird rights, meaning they can exceed the salary cap to re-sign the shooting guard if he decides to decline the 2013-14 option.
The early Bird rights allow the Knicks to pay Smith up to 175 percent of this season's salary, which is $2.8 million. That means the Knicks could offer him a contract for next season at about $5 million, and the agreement could be up to four years with standard raises.
Smith initially deflected a question about his potential free agency on Monday. Later, on "SportsCenter," Smith was asked if he'd like to retire as a Knick.
"Without a doubt. I'm born in New Jersey, born and raised," Smith said. "I would love to retire a Knick."
Information from ESPNNewYork.com's Ian Begley, ESPNLosAngeles.com's Peter Yoon and The Associated Press was used in this report.