The talented Greinke gives the Angels a strong chance to keep alive their hopes of making the postseason, but his mound opponent, Mariners rookie Erasmo Ramirez, has been pitching well and can make it a tough chore for the Halos.
The Angels completed a three-game sweep of the White Sox with a 4-1 victory Sunday to stay 2 1/2 games behind the A's for the second American League Wild Card in the playoffs.
Manager Mike Scioscia is happy the Angels have continued to compete, even with the odds against them.
"You have to keep it going," Scioscia said after Sunday's game. "We don't have a lot of wiggle room right now, and we know what we're up against. I think the guys played a great series here, and we have to start over on Tuesday, create a little momentum, and hopefully it'll lead to a win."
Greinke is 5-2 with a 3.51 ERA since the Angels acquired him from the Brewers at the Trade Deadline and has been strong after a couple of rough first outings with his new team.
He pitched an exceptional eight innings against the division-leading Rangers on Tuesday only to see reliever Ernesto Frieri give up a go-ahead two-run homer to Adrian Beltre in the ninth.
Greinke gave up five hits and an earned run while striking out eight against the Rangers.
His combined record with the Brewers and Angels is 14-6 with a 3.47 ERA in 32 starts.
Greinke took the loss to the Rangers in stride, but, like his manager, he knows with each loss their playoff chances grow dimmer.
"It's tough," Greinke said. "We need to win these games. It's getting close to the end of the season."
Even though he was cruising against the Rangers, Greinke was removed by Scioscia just before reaching the 110-pitch mark, which has become a regular occurrence.
Greinke has surpassed 110 pitches five times in his 11 starts for the Angels but has never thrown more than 115.
"I think he's got a range that he's comfortable in, we're comfortable in, and we're not going to extend anybody," Scioscia explained after Greinke's performance against the Rangers. "We didn't lose this game because of what Zack didn't do out there. He pitched a terrific game, got us to a certain point, and I think when you start to get in a certain range, you want to be careful."
Greinke didn't want to get into specifics about his limits.
"I just pitch as long as I can," he said. "We talked about stuff when I first got here of what I feel best in, and he makes his decision from there."
Ramirez pitched the first eight innings of the Mariners' 4-2 18-inning loss to the Orioles on Tuesday and was dominant, allowing four hits and two earned runs while striking out six.
"Ramirez was fantastic. Threw a great ballgame," manager Eric Wedge said.
For Ramirez, it was another impressive start in what has been limited opportunities.
The Nicaraguan began the season as a long reliever, but the Mariners converted him to a starter in June.
After recovering from a tough couple of starts, Ramirez threw an eight-inning gem, but then injured his elbow during his next outing.
Tuesday was only his third outing since rejoining the team after September callups.
He kept Baltimore batters off-balance with a mix of fastballs in the mid-90s and a sharp command of his off-speed pitches.
"Honestly, the thing was be aggressive in the strike zone, keep the ball down," Ramirez said.
Mariners: Smoak having a good month
First baseman Justin Smoak was 0-for-2 with two walks in Sunday's 3-2 loss to the Rangers, but he's still having an excellent September.
Smoak is batting .345 (16-for-55) with seven runs, four doubles, two home runs and five RBIs in 17 games this month.
Angels: Pujols notches 11th 100-RBI season
Albert Pujols was 3-for-4 with two RBIs Sunday to lift his season total to 101.
That makes 11 times in 12 Major League seasons that Pujols has driven in at least 100 runs.
The only time he failed to reach 100 RBIs was last season.
Scioscia announced his rotation after Sunday's 4-1 win over the White Sox. Following Greinke in the three-game home series against the Mariners will be C.J. Wilson and Dan Haren, respectively. Jered Weaver is slated for Friday's series opener against the Rangers and Ervin Santana would pitch Saturday, on seven days' rest.
The Angels don't have any games left against teams that are ahead of them in the Wild Card race.
After the series with the Mariners, they go to Arlington for three games against the Rangers before finishing the season with three more games against the Mariners in Seattle.