ANAHEIM, Calif. -- Zack Greinke's first pitch in a Los Angeles Angels uniform was lined to left field for a single by Desmond Jennings, who had never faced him in a regular-season game.

Greinke shrugged it off and pitched his usual game, although his run support was nonexistent thanks to Jeremy Hellickson and the Tampa Bay Rays' bullpen. Greinke was outpitched by Hellickson in a 2-0 loss on Sunday, two days after the Angels acquired the 2009 AL Cy Young Award winner from Milwaukee.

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"Hopefully I'll win a bunch of games and it becomes a fun season," Greinke said. "Everything's just happened pretty fast -- traveling here, meeting a bunch of new people, going over things with the catcher and having a day game instead of a night game, which would have made it easier to get adjusted. So a lot of stuff was going on. But once you get on the mound, it's the same game no matter where you're pitching and who it's against."

Greinke (0-1) allowed two runs and seven hits in seven innings and struck out eight. He gave up an RBI single to Matt Joyce in the sixth and threw a run-scoring wild pitch in the seventh after Carlos Pena doubled and advanced on a groundout.

"I made a lot of good pitches -- but some bad ones, too," Greinke said. "I thought my fastball command could have been a lot better. I was pretty upset with the first-pitch curveball to Pena. The wild pitch was just a bad break. No catcher in the world would have stopped that one. You throw a two-strike slider down and hope that doesn't happen."

Greinke, eligible for free agency after the season, was 9-3 with a 3.44 ERA in 21 starts with the Brewers.

"I think everybody was anxious to get him on the mound and see him in an Angels uniform," left fielder Vernon Wells said. "He did what he was supposed to do. We just didn't score runs for him."

Hellickson (6-6) pitched two-hit ball through six innings, striking out five and walking none. He retired 15 of his first 16 batters, allowing only Maicer Izturis' leadoff single in the fourth. The Angels' other hit off him was a leadoff single by Chris Iannetta in the sixth -- a liner that deflected off the glove of diving second baseman Ben Zobrist.

"He's got good stuff," Wells said. "He threw a little harder today than he normally does. He's a good pitcher. He keeps you off-balance and makes you hit his changeup, which is a good one."

Hellickson won despite throwing up five times during the game.

"I just had a little stomach ache and got a little lightheaded there toward the end," he said. "It was hot today, and that was probably the reason. I felt good enough to go out there. I took some stuff before the game, but it kind of caught up with me those last few innings. I felt I had to give us five or six to save the bullpen. My arm felt good, and that's all I really needed."

Hellickson has won consecutive starts for the first time since April 19-25, when he beat the Yankees 9-4 and followed that with a 3-2 victory over the Angels. He was 0-6 with a 4.29 ERA in nine starts preceding these last two outings.

"Throwing strikes was the main thing," Hellickson said. "The last two games I've been attacking the hitters better than I have been. Having no walks is huge for me. I was getting ahead of guys, and the defense was making good plays for me."

Kyle Farnsworth and Joel Peralta followed with a perfect inning each, and Fernando Rodney got three outs for his 30th save in 31 attempts, tying Baltimore's Jim Johnson for the AL lead. With runners on first and second, Rodney fell behind Albert Pujols 3-0 in the count before throwing a called strike and inducing a game-ending, double-play grounder on a changeup away.

"There's a lot of pressure situations out there. So when you've got a guy like Pujols up there, you've got to make your pitch," Rodney said. "I just tried to make a good pitch and get a ground ball with something away. He tried to pull it and I got a ground ball."

Greinke, acquired for Double-A right-handers Ariel Pena and Johnny Hellweg, was prevented from becoming the third major league pitcher in major league history to win 20 consecutive home decisions. Pittsburgh's Ray Kremer won 23 straight from 1926-27 and the Yankees' Lefty Grove 20 in a row from 1938-41. Greinke's previous home loss was with Kansas City on July 26, 2010, when Minnesota beat the Royals 19-1.

"I knew I had a bunch of them in Milwaukee, but I didn't know how many," Greinke said. "It was a pretty lucky streak and a lot of good things happened that were out of my control."

Notes

• Angels rookie Mike Trout, who leads the AL with a .350 average, missed the game because of a sore left knee, injured Saturday night when he tried to make a leaping catch against the fence in left-center field on a home run by Zobrist.
The Angels were shut out in consecutive games for the second time this season, including May 3-4 against Toronto in Anaheim. Their 11th shutout loss tied Oakland for the most in the majors.
In his first game with the Brewers, Greinke lost 8-0 before going 6-0 in his next seven starts.
The Angels begin a 10-game trip with a four-game series at Texas starting Monday night. RHP Ervin Santana will start the opener, his first appearance since July 21, when he gave up six runs and three homers in 1 2/3 innings against the Rangers. He's had a couple of strong bullpen sessions since.