He'll face the A's on Wednesday at Oakland Coliseum in a pivotal American League West matchup that will decide the winner of the three-game set.
The right-hander was solid in his Angels debut, but was roughed up a bit by the Rangers in his last start, surrendering six runs on 10 hits in seven innings of work for a no-decision.
While the Texas heat proved to be too much for Greinke, he takes the mound in Oakland with a career record of 2-0 and 2.25 ERA in four starts there.
"When a guy is as talented as Zack and has achieved what he has achieved, when you see it firsthand, you start to absorb it and see why," Angels manager Mike Scioscia said. "He's definitely a student of the game. He understands his stuff extremely well and I think he competes out there on the mound. He's an intelligent guy. He understands his game."
Greinke and the rest of the Angels will have a tough test in A's right-hander Dan Straily, who is coming off an impressive Major League debut.
Allowing just one run on five hits in six innings of work to the Blue Jays on Friday, he took a no-decision. Also tallying five strikeouts, Straily has 180 strikeouts between the Minors an Majors this season, which is more than any pitcher at any level.
"If you had told me that a year ago when I was fighting for the High-A championship with [A.J. Griffin] that we'd be in a Wild Card race in Oakland, I would have been absolutely baffled by that statement," Straily said after his debut.
As one of three rookies currently in the A's starting rotation, Straily's start on Wednesday will mark the 55th by a rookie this season, 27 of which have been wins.
"I think one thing that you see with Oakland is the talented young arms that come up and have pitched well," Scioscia said. "It always seems like they're rolling over good arms."
Angels: Richards hurts knee in Minor League start
Garrett Richards was forced to leave his start on Monday from Triple-A Salt Lake after just three innings because of left knee soreness.
The right-hander, who's had two stints with the Halos this season, tweaked his knee when running to cover first base, and was lifted as a precaution. While the knee was feeling better after the game, it is still unknown how severe the injury is.
"When a pitcher has to come out of game, obviously there's a concern, but we'll wait until we get some more information to see exactly what's going on," Scioscia said on Tuesday.
A's: Pennington reinstated early
With their bullpen somewhat depleted, the A's reinstated Cliff Pennington from the disabled list earlier than planned Tuesday.
Originally slated to be with the River Cats through at least Wednesday, Pennington's return sent lefty Pedro Figueroa back to Triple-A Sacramento.
"We needed an extra position player," manager Bob Melvin said. "It was difficult to go with just three, and especially with Yoenis [Cespedes] a little banged up, that need was there. The bullpen was in a state of flux for obvious reasons, so even though Pedro Figueroa is going down, he really saved us the last couple of days and has contributed here significantly. It's too bad he has to go down, but nine was just too much in the bullpen. Now we're in a little better shape as far as making moves during the course of a game, with an extra position player."
Yoenis Cespedes was back in the starting lineup Tuesday, having missed Monday's game because of lingering soreness in his right wrist. Trying to be as cautious as possible, Melvin plugged him in at designated hitter. He finished the game going 2-for-5.
"If we can limit him in one of them, hitting or fielding, not have him throw and DH him, we'll probably be further along in getting him to 100 percent, as opposed to being on the field on top of that," Melvin said.
Angels center fielder Mike Trout turned 21 on Tuesday. Trout said he wasn't planning on doing anything fancy, just a dinner with his parents to celebrate. He homered in the loss to the A's, becoming only the fifth player in Major League history to homer on his 21st birthday, joining Ted Williams (1939), Frank Robinson (1956), Alex Rodriguez (1996) and Jason Heyward (2010).
With Tuesday night's game against the A's, Scioscia moved into a tie with Felipe Alou for 50th place in games managed all-time, at 2,055.