NEW YORK (AP) -- Joba Chamberlain mixed in some curveballs and changeups and moved one step closer to getting past the pitch-count limits that have held him back in his first two starts.
All Dan Giese got Sunday was the lineup card and a souvenir ball from a game he'll never forget.
Chamberlain bounced back from a disappointing first start with the Yankees, pitching into the fifth inning to help New York beat the Kansas City Royals 6-3 for its fourth victory in five games.
"As a competitor, you want to be out there as long as you can go and as hard as you can go," said Chamberlain, who opened the year in the bullpen and was limited to 78 pitches on a 95-degree afternoon. "But you also understand that it's a transition. You have to be patient and learn from it and try to get better every time out."
"To have Mariano Rivera close out your first major league win, I stayed out in the dugout to watch it," Giese said. "It was something else."
Rivera allowed a go-ahead homer to David DeJesus in the ninth on Saturday but got the win when the Yankees pushed across two runs in the bottom half for a 12-11 victory. Add in Sunday's rally, and New York has come from behind in nine of its past 11 wins.
Jose Guillen hit a two-run homer and Joey Gathright made three outstanding plays in center field for Kansas City, which has lost 17 of 20. The Royals also dropped to 4-29 at Yankee Stadium since the start of the 2000 season.
"I was pleased with the way we were selective against Joba but once we got into the bullpen maybe it was the change in velocity, the drastic change in velocity, we weren't nearly as balanced," Royals manager Trey Hillman said.
Jason Giambi hit a tiebreaking homer in the sixth and Bobby Abreu finished with an upper-deck home run and three RBIs for the Yankees. Johnny Damon got two more hits after going 6-for-6 with the game-winning single in New York's victory Saturday.
Guillen's third-inning drive put Kansas City ahead 3-2 and gave the slugger three homers and nine RBIs in the last two games.
New York tied it on Abreu's run-scoring groundout in the fifth and went ahead when Giambi led off the sixth with his team-best 14th homer on a full-count pitch from Zack Greinke (5-4).
"It was a slider. It was the fourth one I gave him," Greinke said. "The others he just fouled off. That one he just kept right there."
Chamberlain allowed three runs -- two earned -- and five hits in 4 1/3 innings, striking out five and walking one. He could be extended to around 90 pitches for his next scheduled outing Friday at Houston.
"It was a positive day," Yankees manager Joe Girardi said.
The 22-year-old Chamberlain made his highly anticipated first major league start Tuesday night and a sellout crowd gave him a standing ovation before he threw his first pitch. It quickly went downhill from there as he walked four and lasted just 2 1/3 innings in the Blue Jays' 9-3 victory.
His second start had a much different feel.
The fans cheered from their seats as the hard-throwing right-hander fired a called strike on his first pitch to DeJesus. Chamberlain allowed a one-out single to Mark Grudzielanek but got through the first in 13 pitches.
Chamberlain, who labored through a 38-pitch first against Toronto, set the Royals down in order in the fourth and left after issuing a one-out walk to DeJesus in the fifth.
"I think he learned a lot from his first start," said Giambi, who also made a key diving catch at first base. "He attacked the hitters a lot more this time around."
Chamberlain, the 41st overall pick in the 2006 amateur draft, was converted to a reliever last year to help the Yankees bridge the gap to Rivera. Chamberlain made his major league debut at Toronto on Aug. 7 and went 2-0 with a 0.38 ERA in 19 games.
He opened this season in the bullpen but was stretched out over three appearances before he joined the rotation. He threw 62 pitches against Toronto.
Greinke allowed four runs and six hits in five-plus innings for the Royals.
The Royals optioned RHP Joel Peralta to Triple-A Omaha before the game and purchased the contract of RHP Jeff Fulchino from their top farm club. Fulchino pitched a scoreless eighth in his Kansas City debut. ... Umpire Jerry Layne was released from the hospital Sunday and said he was OK. Layne sustained a mild concussion when he took a foul bunt off his mask while working the plate in Saturday's game. Mike Estabrook replaced him Sunday and served as the second base ump. ... The 95-degree temperature was a season high for Yankee Stadium. ... Gathright was sore after his big day in the field and might sit out Monday.