CLEVELAND -- Corey Kluber figured out a way to pitch around the lack of run support from his teammates: Don't give up any runs at all.

Kluber pitched 6 2/3 scoreless innings Tuesday night to earn his first victory in more than a month, and the Cleveland Indians beat the Houston Astros 2-0 at Progressive Field.

"Anytime you win, it's always better than the alternative," said the right-hander, whose previous win came on May 28.

Kluber struck out seven and walked two while lowering his ERA to 3.45, which doesn't seem to go with his 4-9 record.

That record is deceiving because his run support has been almost non-existent. In six starts between victories, Kluber was 0-4 with 3.86 ERA, with the Indians scoring a total of six runs during the four defeats. For the season, Kluber has received an average of 2.4 runs per game of support. Cleveland scored three runs or fewer in 16 of his 18 starts.

Kluber made two runs stand up Tuesday.

When asked about Kluber's perseverance despite the lack of support, Indians manager Terry Francona lauded the reigning American League Cy Young Award winner's will to compete.

"We played a good game," Francona said. "We didn't knock the ball all over the park, but we played good enough to win."

Designated hitter Michael Brantley had three hits, including a home run, to lead what little offense Cleveland generated against Vince Velasquez (0-1). The Astros right-hander held the Indians to two runs in 6 1/3 innings.

"It was a well-pitched game on both sides," Houston manager A.J. Hinch said. "We put up some really good at-bats against a really good pitcher and had nothing to show for it. We had a hard time getting anything started against Kluber."

Cleveland led 2-0 when Brantley hit a solo home run into the seats in right field leading off the sixth inning against Velasquez. It was his fifth home run of the season, his first since May 14. Brantley went 180 at-bats between home runs.

Kluber was removed from the game in the seventh inning when his first career balk, a passed ball and a walk put runners at first and third with two outs. Kluber was at 119 pitches, so Francona called for right-hander Zach McAllister from the bullpen.

McAllister struck out second baseman Jose Altuve to end the inning, then pitched a scoreless eighth.

Right-hander Bryan Shaw pitched the ninth inning to pick up his second save. Shaw was subbing for closer Cody Allen, who got the day off due to a stiff back.

First baseman Carlos Santana and left fielder David Murphy each had two hits for Cleveland.

Houston got two hits each from right fielder Preston Tucker and designated hitter Evan Gattis.

Cleveland took an early lead after Velasquez retired the first two batters in the bottom of the first inning. Brantley singled to right field. Murphy followed with a double to right field, scoring Brantley.

Although one run was enough for Kluber on this night, the Indians added a second run on Brantley's sixth-inning blast.

"We had a small margin of error with Kluber," Hinch said. "It turned out to be no margin for error. We couldn't touch him."

Kluber said, "The big key for me tonight was working ahead in the count and pounding them inside in the strike zone because I thought they had comfortable at-bats against us last night."

NOTES: Indians 1B Carlos Santana, hitting just .207, was dropped to the No. 7 spot in the order, the lowest he has hit in the lineup this season. Santana came into the game batting .118 (2-for-17) in July, but he went 2-for-3. ... Indians 2B Jason Kipnis' 29-game home hitting streak was snapped when he went 0-for-3 with a walk. Kipnis' streak is the second-longest home hitting streak in Indians history. Hal Trosky hit in 31 consecutive home games in 1936. ... LHP Dallas Keuchel is the first Astros pitcher selected to the All-Star team since Roy Oswalt in 2007.