Both pitchers have recorded wins in three of their last four starts -- over which they've combined for a 1.69 ERA (11 earned runs over 58 1/3 innings).
The Rangers hold a four-game lead over the second-place A's in the American League West, while the Halos are 3 1/2 games back of Oakland for the second AL Wild Card spot.
Darvish comes in 4-1 in his past six starts, with Texas grabbing victories in five of those games. The right-hander has gone at least seven innings while giving up three or fewer hits in each of his past three starts, and is the only pitcher in baseball to accomplish that feat this season.
"If he rattles off five or six good ones down the stretch, they forget about all that other stuff," Rangers manager Ron Washington said. "That's what baseball is about: What have you done for me lately?"
Greinke, meanwhile, got off to a slow start with his new club, posting a 6.19 ERA and 1-2 record in his first five starts with the Angels.
But since then, Greinke is 4-0 with a 1.70 ERA in five starts.
What's made Greinke more effective of late?
"Commanding all of my pitches for the most part, and not having to worry about if I'm going to be able to throw it where I want," he said. "So I can kind of think about where to throw it and what to throw, instead of just trying to be able to throw it where I want to."
Rangers: Hamilton misses a game
The Rangers were without Josh Hamilton for Wednesday's game, as the slugger left Tuesday night's game with vision issues. Hamilton saw an internist on Wednesday and nothing "definitive" was found, Rangers general manager Jon Daniels said.
Hamilton won't return until he has clarity of vision, according to Washington.
"Because it's dangerous," Washington said. "Being able to see is important."
Mike Napoli continues to hurt his former team, going 1-for-3 with an RBI double in Wednesday's 6-2 win over the Angels. He is now hitting .455 (20-for-44) with four home runs and 10 RBIs in 14 games against the Halos this season.
Angels: Pujols returns to the team
Albert Pujols returned to play first base for the Angels on Wednesday after missing Tuesday's series opener to stay in the hospital with his wife, Deidre, and the couple's newborn child, Esther Grace.
He went 2-for-4 on Wednesday.
"Obviously I wasn't here, but my ballclub was playing," Pujols said. "I wish I was here, but you know what, it wasn't something I could control. I had to attend to my family first and make sure everything was good so I can refocus and finish strong the next couple of weeks."
Erick Aybar's .376 average (59-for-157) since the beginning of August leads baseball.
Michael Young went 2-for-5 in Wednesday's game, extending his hitting streak to eight games.
Mike Trout broke Devon White's Angels rookie record for total bases in a season on Wednesday with his 284th on a leadoff single in the fist.