Beltre's fourth hit Tuesday put the Rangers in position to win in the bottom of the ninth inning a night after Fielder pulled them within a half-game of the Astros with a tiebreaking two-run home run with Beltre aboard in the eighth.
Mitch Moreland's sacrifice fly finished the 6-5 victory Tuesday night.
Eight games back and in third place in the division after losing on Aug. 1, the Rangers have gone 27-14 since. They've won five straight over the Astros, who had been in first place since July 28. Texas won the first two of this four-game series.
"They have fought, scratched, clawed all ways imaginable to get to this point," first-year manager Jeff Banister said. "We're not done yet. Still got a long ways to go."
Fielder opened the ninth with a single to left off Oliver Perez (0-2), and pinch runner Drew Stubbs went to third on a single from Beltre, who drove in two runs with a single in the first and a tying double in the fourth.
"If I make the absolute perfect throw, I might have a chance at Stubbs," said Rasmus, who had moved over from left field in the eighth. "He can fly. I might have tried too hard to make the perfect throw instead of just throwing it."
Texas closer Shawn Tolleson (6-3) pitched a scoreless ninth as the Rangers (77-67) moved into sole possession of first place for the first time this year, at a season-high 10 games over .500.
The team, citing Elias, said the Rangers joined five teams since 1969 to take the first division lead this late in the season. The most recent was Oakland in 2012 when the A's finished a three-game sweep of the Rangers on the final day of the regular season to win the AL West.
"We're not going to look at us being in first or wherever we're at right now," Moreland said. "We've still got a couple of weeks left in the regular season, and we're going to continue to focus on each game."
Houston (77-68) holds the second AL wild card, 1½ games ahead of Minnesota after the Twins lost to Detroit 5-4. The Astros have lost six of eight on the road trip and have one of the worst road records in the AL at 29-44.
"This is really intense baseball," Astros manager A.J. Hinch said. "It's fun to do it; it's not fun to lose. I felt we deserved a little better fate."
Texas starter Derek Holland couldn't hold a 4-0 lead after the first, immediately allowing the first four hitters to reach in the second before Jake Marisnick's sacrifice squeeze bunt scored Jonathan Villar to get the Astros to 4-3.
Evan Gattis finished the rally in the fourth with a two-out, two-run single for a 5-4 lead. His soft two-strike liner over leaping shortstop Elvis Andrus kept Holland from escaping after the Astros put runners at the corners with nobody out.
Astros: 3B Jed Lowrie was out of the lineup after getting banged up on consecutive pitches in Monday's series opener. He fouled a ball off his left shin, and then got hit by a pitch on his left foot. He ended up leaving the game. Hinch said he wasn't sure if Lowrie would be available off the bench. ... CF Carlos Gomez (left rib muscle) rejoined the team Tuesday after being scratched from the lineup Sunday at the Los Angeles Angels and getting evaluated Monday in Houston. Hinch said he was day-to-day.
Astros: LHP Dallas Keuchel (17-7, 2.22 ERA) has allowed three runs in 22 innings over three starts against the Rangers this season. He has just one win, though -- 10-0 on July 19.
Rangers: LHP Martin Perez (2-5, 5.43) got an extra day of rest when the Rangers moved Holland in front of him in the rotation, which also helped Texas line up the pitching staff for the postseason.
- Home Plate Umpire - Phil Cuzzi
- First Base Umpire - Gabe Morales
- Second Base Umpire - Tony Randazzo
- Third Base Umpire - Gerry Davis