Jimenez returned to Houston on Friday night in a different uniform, but the result was the same.
Jimenez (7-5) allowed four hits with eight strikeouts in 6 2/3 innings to improve to 4-0 with a 1.88 ERA in six career starts against Houston.
"It's really a nice place to pitch," he said. "It's warm, everything breaks. So it's fun to pitch here."
The victory is Cleveland's fourth straight, which ties a season high and extends its lead in the American League Central to 1½ games. Three of those four wins have come by one or two runs, a stat Indians manager Manny Acta likes.
"When you win those ballgames, it's a good sign," he said. "It means that you can't go back into the game and look at mistakes that you made that cost you the game."
Choo's triple was one of only two hits the Indians managed in seven innings against Houston starter Lucas Harrell (6-6) as these teams met for the first time since 2001.
Acta was impressed with Harrell, but he also liked what he saw from his starter.
"Harrell was just very tough, he pitched very well, but Ubaldo was also very good," Acta said. "(Jimenez) had good off-speed stuff, especially the split-finger fastball. He had better command of his fastball later in the game and just did a very nice job."
Choo helped make it 1-0 when he scored on a sacrifice fly by Asdrubal Cabrera after his triple.
Brantley added an insurance run for the Indians with his RBI single with one out in the ninth inning.
Chris Perez struck out the side in the ninth to complete Cleveland's sixth shutout this season and give him his major league-leading 23rd save.
Harrell took the loss despite allowing two hits and striking out a career-high nine in seven innings.
"The location of his fastball was pretty impressive," Houston manager Brad Mills said of Harrell. "That was the biggest thing. He stayed aggressive with his fastball. He was making really good pitches on it."
Including Cabrera's out, Harrell retired 19 of the next 20 batters he faced. Cleveland's only base runner in that stretch came on a walk by Carlos Santana with two outs in the fourth.
Harrell didn't run into trouble until Santana and Brantley drew consecutive walks with one out in the seventh inning, before a single by Johnny Damon loaded the bases.
The Indians finished with four hits to end a streak of four straight games with at least 10 hits.
The Astros had several opportunities to score but were unable to connect at key times for the second straight game, going 1 for 7 with runners in scoring position. They went 1 for 12 with runners in scoring position in a 2-1 loss to the Royals on Wednesday.
Chris Johnson singled in the fifth but was out at second when Snyder grounded into a force out. An error by Cabrera let Snyder take second before Harrell singled. Jimenez came out unscathed again when he retired Jose Altuve before striking out Schafer to end the inning.
Bogusevic doubled to left field to start Houston's seventh. Johnson and Snyder both grounded out before a walk by pinch hitter Justin Maxwell chased Jimenez.
Reliever Joe Smith took over and struck out Altuve to leave the Astros empty-handed yet again.
Brantley then singled to score Cabrera. Bogusevic scooped up the hit by Brantley and threw to the plate, but the high throw bounced off Snyder's glove and rolled away, sending Kipnis for home. But Snyder got the ball to Lee, who was covering home, to tag him out.
Houston starter Bud Norris, on the DL with a sprained knee, is scheduled to make a rehabilitation start for Triple-A Oklahoma City on Saturday. ... Houston OF Maxwell had an MRI on Thursday that revealed what manager Mills called a "loose body" in his left ankle. He wasn't in the starting lineup, but pinch-hit in the seventh inning.