"Yeah, we're feeling great right now, but can't stop playing the way we're doing right now because we're getting close," Andrus said. "We're pretty confident."
"I think you can't help but feel it. We also believe in the fact that these guys are in the now ... no opportunity wasted," first-year Texas manager Jeff Banister said. "They really don't get caught up with what's down the road, but I believe that it brings a sense of energy and a little added energy for us, and some added focus."
Adrian Beltre hit the first of three Texas home runs in the win over the Tigers.
Robinson Chirinos and Mike Napoli also went deep for the Rangers (86-72), who open that final regular-series at home against the Angels on Thursday night. Los Angeles lost 8-7 Wednesday against Oakland to fall three games back in the division.
Houston, with the same 83-75 record as the Angels, played at Seattle later Wednesday night.
The Rangers won the AL West title in 2010 and 2011 on way to their only World Series appearances. They lost the AL's first one-and-done wild-card game at home in 2012, then dropped a wild-card tiebreaker at home in 2013 before losing 95 games last season.
Yovani Gallardo (13-11) allowed nine hits over 5 1/3 innings, but gave up only two runs to win for the first time in his last four starts. The right-hander struck out five and walked one.
Detroit took a 2-0 lead in the first inning for the second night in a row, this time on a two-run double by Tyler Collins.
Texas got even in the bottom of the first on Beltre's 17th homer, a shot to left-center field. Beltre has an AL-best 29 RBI in September, and 74 for the season.
Chirinos led off the second with his 10th homer, putting Texas ahead to stay. Beltre had a two-out double off the left-center wall and scored on Prince Fielder's bloop single before Napoli hit a blast to the wall behind the lower deck of seats in left field.
Beltre is hitting .416 (32 of 77) in his last 19 games, raising his season average from .261 to .283.
"The captain, the guy that sits right in the middle of our club, beacon that all these guys look towards," Banister said.
Tigers left-hander Matt Boyd (1-6) allowed all three Texas homers while giving up seven hits in 2 2/3 innings. He struck out two and walked one.
"My changeup usually doesn't get hit that hard. It wasn't the only thing that was hit," Boyd said. "I wasn't really staying with my delivery. Didn't have the rhythm like I've the past three outings."
Shin-Soo Choo, who singled and scored before Beltre's homer in the first, has an eight-game hitting streak and is batting .444 (24 of 54) over his past 14 games. He has reached base in 49 of his last 51 games.
Gallardo matched his career high by making his 33rd start. He became the sixth pitcher to make at least 30 starts and throw 180 innings the past seven seasons. One of the others is teammate Cole Hamels.
Tigers: Victor Martinez missed his second consecutive game with a sore left quad. ... 3B Nick Castellanos was back in the lineup after coming out in the first inning Tuesday because of a bruised right finger and sore left wrist.
Rangers: C Robinson Chirinos made only his second start since being activated from the disabled list Sept. 7 after missing more than a month with a left shoulder strain.
Tigers: After its final off day of the season, Detroit opens a three-game series Friday night at the Chicago White Sox.
Rangers: LHP Derek Holland, 0-2 with an 8.59 ERA his last four starts, pitches the series opener against the Angels.