Haren tries to continue his recent superb pitching when the Angels face the Oakland Athletics in the middle game of a series Tuesday night in Anaheim.
Los Angeles (76-80) got Haren (3-4, 2.85 ERA) in a five-player trade from Arizona on July 25, when it harbored hopes of catching Texas in the division race.
The Angels haven't come close to putting any pressure on the Rangers, who have already clinched the West title.
Los Angeles now must compete with the A's (77-79) for second, and needs to win five of its final six games to avoid its first losing record since 2003.
"When you're playing professional ball, you never give up as long as you're on the field," right fielder Torii Hunter said. "We've got to win five out of six, and that's our goal. I mean, our real goal was to take over first place, and that didn't work out. So now we have another plan - to finish at .500. But saying 'I want to grab second place' doesn't sound good."
Though Los Angeles will fail to win its sixth West crown in seven years, Haren is certainly not to blame.
The right-hander has received three runs or fewer in 11 of 12 starts for his new club. He has compiled a 1.32 ERA over his last six outings, but has only two wins to show for it.
Haren, who had 43 wins with the A's from 2005-07, is 1-0 with a 3.86 ERA in two starts against his former club.
Facing Oakland could provide Haren some rare support. Los Angeles has outscored the A's rival 26-8 while winning the last four meetings in Anaheim, including Monday's 6-5 victory that ended a four-game overall losing streak for the Angels.
The A's are trying to avoid matching their season-high five-game slide from May 12-16. They need to win five of six to finish with a winning record for the first time since 2006, when they last won the West.
Another strong start from Dallas Braden (10-13, 3.49) could move them within one game of .500.
The left-hander was superb last Thursday, tossing eight one-hit innings while striking out seven in a 5-0 victory over the Rangers. He had lost each of his previous four starts, compiling a 6.23 ERA while pitching through the sixth inning just once.
"It was classic Dallas when he's on," manager Bob Geren said. "He had a great changeup and used it in all different counts."
Braden is 2-5 with a 4.82 ERA in seven starts against the Angels.