Price barely beat out 2011 winner Justin Verlander for the American League prize in one of the closest votes ever. Dickey was an easy choice for the NL honor in balloting by the Baseball Writers' Association of America.
The 38-year-old Dickey became the first knuckleball pitcher to win the Cy Young Award, an achievement mentors such as Hall of Famer Phil Niekro are quite proud of.
"I am not a self-made man by any stretch of the imagination," Dickey said on MLB Network. "This is a victory for all of us."
Runner-up two years ago, Price was the pick this time by the slimmest of margins. He received 14 of 28 first-place votes and finished with 153 points to 149 for Verlander, chosen first on 13 ballots.
Other than a 1969 tie between Mike Cuellar and Denny McLain, it was the tightest race in the history of the AL award.
Rays closer Fernando Rodney got the other first-place vote and came in fifth.
"It means a lot," Price said. "It's something that I'll always have. It's something that they can't take away from me."
Price went 20-5 to tie Jered Weaver for the American League lead in victories and winning percentage. The 27-year-old lefty had the lowest ERA at 2.56 and finished sixth in strikeouts with 205.
Verlander, also the league MVP a year ago, followed that up by going 17-8 with a 2.64 ERA and pitching the Detroit Tigers to the World Series. He led the majors in strikeouts (239), innings (238 1-3) and complete games (six).
Price tossed 211 innings in 31 starts, while Verlander made 33. One factor that might have swung some votes, however: Price faced stiffer competition in the rugged AL East than Verlander did in the AL Central.
"I guess it's a blessing and a curse at the same time," Price said. "There's not an easy out in the lineups every game. It feels like a postseason game."
Weaver came in third with 70 points, but was listed second on a pair of ballots. The right-hander threw a no-hitter and had a 2.81 ERA in his first 20-win season but missed time with injuries and totaled only 188 2-3 innings for the Los Angeles Angels.
The top pick in the 2007 amateur draft out of Vanderbilt, Price reached the majors the following year and has made three straight All-Star teams.
Despite going 19-6 with a 2.72 ERA in 2010, he finished a distant second in Cy Young voting to Felix Hernandez, who won only 13 games for last-place Seattle but dominated most other statistical categories that year.
Verlander was trying to become the first AL pitcher to win back-to-back Cy Youngs since Boston's Pedro Martinez in 1999 and 2000. San Francisco right-hander Tim Lincecum did it in the National League in 2008-09.
Dickey garnered 27 of 32 first-place votes and easily outdistanced 2011 winner Clayton Kershaw of the Los Angeles Dodgers. Gio Gonzalez of Washington finished third.
Dickey joined Dwight Gooden (1985) and three-time winner Tom Seaver as the only Mets pitchers to win the award. The right-hander was the club's first 20-game winner since Frank Viola in 1990. And perhaps most impressive, Dickey did it during a season when the fourth-place Mets finished 74-88.
"It just feels good all over," he said.
Price and Dickey are both from Tennessee, making them the fourth pair of Cy Young winners to be born in the same state, according to STATS.
The two MVP awards will be announced Thursday. Verlander's teammate, Triple Crown winner Miguel Cabrera, is a leading contender in the American League.
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