Rays’ 2-0 win spoils Zack Greinke’s debut with Angels

Adding Zack Greinke to solidify the starting rotation may ultimately carry the Angels to the heights they seek.

Now they need to rediscover their offense.

Tampa Bay starter Jeremy Hellickson and three relievers combined for a 2-0, four-hitter Sunday, and the Angels are saddled with a 23-inning scoreless streak as they open a four-game American League West showdown series at Texas on Monday.

The Angels got singles by Maicer Izturis and Howie Kendrick against closer Fernando Rodney with one out in the ninth inning, but Albert Pujols grounded into a game-ending double play.

“We have to work to get in a better groove,” said Angels cleanup hitter Mark Trumbo, who was 0 for 3.

From another perspective, Angels catcher Chris Iannetta expressed enthusiasm for what it’ll mean to have Greinke take the hill every fifth day from now into October.

“He never gave in to anybody, no matter what the count or the situation,” Iannetta said.

Despite watching his streak of consecutive home victories end at 19, Greinke provided a rich account of the intense consistency he is known for, striking out eight and compiling a string of 10 consecutive outs during his 111-pitch, seven-inning Angels debut.

“My fastball command could’ve been better in some big moments, but I made a lot of good pitches,” Greinke said.

The 2009 American League Cy Young Award winner, acquired from the Milwaukee Brewers on Friday in exchange for shortstop Jean Segura and minor league pitchers Ariel Pena and Johnny Hellweg, was in a scoreless duel with Hellickson (6-6) until the sixth inning.

Then, Tampa Bay cleanup hitter Matt Joyce hit a two-out single to right field to drive in Sam Fuld.

Greinke said he wanted the pitch to Joyce to be down and away “and it was middle and away.”

Carlos Pena hit a leadoff double in the seventh inning, and on a 1-and-2 pitch one out later, Greinke threw a curveball that broke a foot in front of the plate for a wild pitch that bounced over Iannetta and allowed Pena to score from third base.

Typically, that kind of outing is good enough for a victory, with the Angels ranking fourth in the major leagues in home runs this month and scoring three or more runs in 17 of their last 23 games.

But Tampa Bay pitchers have given up only eight runs in six games against the Angels.

And Angels offensive catalyst Mike Trout sat out Sunday after suffering a bruised left knee Saturday. Trout said he’ll be ready to start Monday.

That, combined with the expected 12 starts Greinke will make between now and the end of the regular season, was cause for optimism in the manager’s office.

“Zack pitched terrific,” Mike Scioscia said. “And he gave us a chance to win.”

lance.pugmire@latimes.com

twitter.com/latimespugmire