The win snapped a frustrating four-game losing skid and earned the Tribe its 30th victory since the All-Star break.
"We're trying to finish the year strong these last two weeks," said manager Terry Francona. "We're showing up every day to win and meet our goals, period."
Altuve may have been the star of the show, tallying a pair of hits to tie and ultimately surpass Craig Biggio's Astros record of 210 hits in a single season, set in 1998. But it was Kluber who was the true difference maker for the result.
Prior to the game, Indians general manager Chris Antonetti spoke to the media and pleaded his case for the righty to be a serious Cy Young Award candidate.
Kluber made Antonetti look like a prophet hours later, as he struck out a career-high 14 hitters and overcame a couple rugged innings to finish with seven innings of one-run ball.
"Today, he had to work into it, but once he did ... it was electric even though I thought [the Astros] did a good job," Francona said. "His stuff is just so late-moving. There's a reason he has all those strikeouts."
It was the most strikeouts by a Cleveland hurler since Bartolo Colon fanned 14 Blue Jays in May of 1998. Kluber now has 244 strikeouts this season, already good enough for 12th on the team's single-season list.
"There were times tonight we needed strikeouts, not just outs," Francona said. "He looks as strong as ever."
The Astros still recorded seven hits off Kluber, and he had to finagle out of a bases-loaded jam in the fourth inning.
"I didn't consistently execute throughout the game, but I did at the points when we needed it," Kluber said. "Yan kind of led me through the early part and then backed me up."
One inning later, Altuve tied Biggio's mark with a scorching chopper down the third-base line. He broke it off Kluber with a seeing-eye grounder up the middle in the seventh.
Kluber backed off after the record breaker, giving Altuve his moment even though the single moved a runner into scoring position and brought the tying run up to the plate.
"That's a big accomplishment for him to have more hits than anybody in the history of that franchise," Kluber said. "You let him enjoy that."
Just like Kluber stopped that rally and many other Astros threats, he may as well be the Indians stopper this season. Tuesday's outing marked the fourth time this season Kluber has delivered a win with the team mired in a four-game losing streak.
"Like I told some of the coaches in there, it was probably one of the better games I've ever seen pitched," said Astros interim manager Tom Lawless. "He was real good. He's one of the best [Major League] pitchers."
For the second straight day, the Indians provided some early run support. Carlos Santana was again the culprit, driving in a run on a fielder's choice groundout.
Unlike Monday night's offensive struggle, Cleveland found just enough success against Astros starter Nick Tropeano and a mix of Astros bullpen arms.
With Lonnie Chisenhall on first and two outs in the fourth, Gomes singled to left-center field. Astros outfielder Robbie Grossman mishandled the ball and Chisenhall jetted home for a 2-1 lead.
Gomes extended that lead with a laser two-run homer that barely cleared the left-field fence in the sixth for his 19th dinger of the year.
Meanwhile, the Astros only managed a first-inning run off Kluber and couldn't capitalize on some prime opportunities while leaving 10 men on base.
Kluber is now 3-0 with a 1.65 ERA in three career appearances against the Astros, as he racked up his ninth outing with 10 or more strikeouts this season.
Relievers Bryan Shaw and Cody Allen combined to close the game out and strike out three more batters to give the Indians a season-best 17 for the game.
The teams are halfway through this four-game set in Houston, and the Indians have now regained the season series lead at 3-2.
With Altuve's mark in the books and Cleveland back on the winning side of things as it chases down slim playoff hopes, the Indians won't be playing spoiler again.
"Tonight was nice, but it won't do us any good tomorrow," Kluber said. "Until we're mathematically eliminated, we have a chance."