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Atlanta's Chris Johnson went 0 for 4 against Philadelphia and slipped to .321 -- effectively locking up Cuddyer's first batting title in 13 big league seasons with one game remaining.
"It means a lot," said Cuddyer, who was a teammate of two-time AL batting champion Joe Mauer in Minnesota.
"It takes a lot of hard work, sticking to routines and things of that nature -- and a lot of luck along the way, too. I'm not too proud to admit that to do something like that, you've got to get lucky.
"I went into the season a career .271 hitter. So and to be in a position like this, I never would have thunk it," Cuddyer added. "I never thought that when the season ends, I'd be on top. I've never been in that position before, so I was never assuming that I was going to be there.
"Obviously when you get into September and you're in contention, you keep plugging away for it. And fortunately, I've had a good September. But I never tried to get ahead of myself."
Cuddyer is hitting .313 outside of Denver, so he's not just benefiting from playing half of his games at Coors Field.
"To lead the league in hitting you have to hit well at home and on the road -- unless you hit like .400 at home," he said. "I've been in this organization only two years, so I've never really taken that home-road thing to heart, as far as Coors Field is concerned."
Nicasio (9-9) allowed three hits over 5 1/3 innings and struck out seven while winning for the first time since Aug. 26 against San Francisco. The last time the 27-year-old right-hander faced the Dodgers on July 12 in Los Angeles, he outpitched Clayton Kershaw with seven scoreless innings for the victory.
"That's the thing about Juan. He can step up and have a performance like that," Rockies manager Walt Weiss said. "He was trying to find consistency after being out for much of the time over the last two years. We've seen that from him earlier this year when he matched up with Kershaw and threw much like that."
It was only the fifth shutout win for the Rockies.
"It's just good to go out there and play a competitive game like that and end up winning a really tough game against a really good team," Weiss said. "I'm proud of the way our guys have played down the stretch. We fight until the last out, and we're going to fight until the last out of the season."
Greinke (15-4) allowed a run and four hits through six innings. The right-hander struck out seven and did not allow a walk in his 300th major league game. Troy Tulowitzki doubled with one out in the fourth and scored on Arenado's two-out double to left-center.
Greinke lost for the first time in eight decisions since July 25 and finished his first regular season as a Dodger with a 2.63 ERA in 28 starts. He is scheduled to start Game 2 of the Division Series.
With Andre Ethier's status for the playoffs in doubt because of shin splints, three other high-profile Dodger outfielders also were missing from the lineup.
Center fielder Matt Kemp was a late scratch because of left ankle soreness, and Carl Crawford was rested by manager Don Mattingly. Rookie Yasiel Puig, who fouled a pitch hard off his left shin and left Friday's game after five innings, pinch-hit in the seventh and struck out.
"He was begging to get out there tonight once Matt couldn't go," Mattingly said of Puig. "But I felt like there was no reason for it, being that last second. We didn't know about Matt 'till five minutes before the game."
Greinke is averaging 1.86 walks per nine innings in his past 16 starts, after tying a career worst with seven bases on balls at Colorado on July 3. He finished with 19 hits, the most by a Dodgers pitcher since 1993, when Orel Hershiser was 26 for 73. ... Kershaw was presented with the team's eighth annual Roy Campanella Award by former manager Tommy Lasorda before the game.