The Rangers need just one win in this doubleheader in Arlington to wrap up a playoff spot, while Trout and the Angels have little margin for error with five games left.
Rain wiped away Saturday's game to force a split twinbill on Sunday, but one game that did take place hurt both Texas (92-65) and Los Angeles (87-70). Down 4-2 in the bottom of the ninth, Oakland rallied to force extra innings, then won 7-4 in the 10th to pull within 2½ games of Texas for the AL West lead while extending its wild-card cushion over the Angels to 2½.
Getting swept Sunday along with another A's win would end Los Angeles' postseason hopes.
"Obviously every time they win, it puts them closer to where they want to be, and the help we're looking for hopefully will come at some point," Angels manager Mike Scioscia said. "We've got five games. From some perspective it seems like it's a blink of an eye. Another perspective, it seems like it's a lifetime.
"We have to put up wins, that's what we need to do. Hopefully we'll get the opportunity to get our toe in the door."
"I want to get (Darvish) out there as soon as we can," said Rangers manager Ron Washington, who bluntly said "I don't like them" when he was informed his team would have to play a doubleheader Sunday.
The Angels likely feel the same way. Should they wind up in a one-game playoff Thursday, either Greinke or Santana would now be starting on short rest.
Washington may not be looking forward to a long day at the ballpark, but he should be happy to see Darvish pitch. The right-hander is 4-0 with a 1.46 ERA in his last five starts, including eight innings of four-hit ball in a 3-1 victory at Anaheim on Sept. 20.
The Angels are hitting .174 off Darvish in five games, and they've struck out 41 times in 31 2-3 innings. Trout has fanned in five of his 14 at-bats against Darvish, but he's walked three times and has four hits -- including a homer.
Trout, who led off Friday's 7-4 win with a homer and later tripled, is hitting .348 with six homers, 19 RBIs, 23 runs and 16 walks in 24 career games in this series.
The rookie is only hitting .255 in September but still has an impressive MVP resume.
"It's definitely been a long year, but these games, when they mean the most, the adrenaline rush kicks in," Trout told the team's official website. "Especially here, it's sold out every night, and (the Rangers are) doing everything they can to knock us out and we're doing everything we can to knock them out."
Though facing Darvish won't be easy, the Angels should feel confident with Greinke on the mound. The right-hander is 5-0 with a 1.62 ERA in his last seven starts, and in Tuesday's 5-4 win against Seattle became the first pitcher in the live-ball era to strike out 13 in a five-inning outing.
Greinke went much deeper in his only start this season against Texas, holding the Rangers to a run and striking out eight over eight innings while opposing Darvish on Sept. 20.
Holland, who's 4-0 with a 3.24 ERA in his last nine starts, got the best of Trout and the Angels on Sept. 19, yielding two runs in seven innings of a 6-2 road win. He had given up 12 runs over 13 1-3 innings in his first two 2012 starts versus Los Angeles.
Santana is 5-2 with a 3.08 ERA over his last 10 starts. The right-hander has been even better in his past four, compiling a 2.03 ERA with 32 strikeouts in 26 2-3 innings while winning two of three decisions.
"He's stepped it up in the last three or four starts," right fielder Torii Hunter said. "He's showing people he's still got it."
Santana was especially terrific in his latest outing, allowing one run and two hits while fanning a season-high 11 over seven innings Sept. 21 in a 6-2 win over Chicago.
He's received a lot of help while winning his last two games in Arlington, posting a 5.25 ERA but being backed by 20 total runs. Santana allowed three runs in five innings of a 15-8 victory there July 30.
Copyright 2012 by The Associated Press
This story is from ESPN.com's automated news wire. Wire index
MORE MLB HEADLINES
- Yanks' Teixeira tests leg, 'couldn't be happier'
- Sizemore's scoop caps Yankees' triple play
- Mattingly voices worry over threats to Puig
- Dodgers' Ramirez hit on hand, misses game
MOST SENT STORIES ON ESPN.COM
- Majestic Triple Peak Men's Texas Rangers Derek Holland Royal T-Shirt