HOUSTON -- With his family in attendance from his hometown of Round Rock, just north of Austin, Chicago White Sox left-hander John Danks had no plans of surrendering the baseball or the mound even after the Houston Astros mounted a modest threat in the bottom of the ninth inning.

Danks recorded his first complete game since 2011 and blanked the Astros 6-0 on Sunday at Minute Maid Park, leading the Chicago White Sox to victory in the rubber match of this three-game series.

Danks (3-4) posted his first complete game since Aug. 27, 2011, against Seattle while also recording his third career shutout. He had surrendered 11 earned runs over his last two starts and 10 1/3 innings, but against the Astros (31-20), Danks was in control from the first pitch.

"That's fun," Danks said. "I hadn't been back in Texas since Christmas. It's nice to have friends and family and people who care about me here. I hadn't had a whole lot of luck with family in town, so maybe I broke that curse too. Very satisfying to have a good game and get a win.

"It's good. I've been saying for the last five days that I need a good one. It's just the last couple I've struggled. Hopefully this will jumpstart a nice little run. That's the goal every time out. Go as deep as possible and give us a chance to win. These guys scored plenty of runs, enough to kind of let us relax."

Danks scattered 10 hits and matched his season high of 118 pitches, including 82 strikes. He walked one batter and posted six strikeouts.

"Command-wise, when he can throw his fastball and place it in there and get a strike, and then take a little off and get them swinging out front (he's effective)," White Sox manager Robin Ventura said of Danks. "It's an aggressive group over there. He has to be able to be around the zone and be able to commit them swinging-wise on his off-speed stuff. He was good fastball-wise in the zone."

The White Sox (23-26) provided early run support against Houston right-hander Roberto Hernandez, scratching across one run on three singles in the second inning before expanding their lead to 4-0 with a three-run third inning.

Center fielder Adam Eaton (single), left fielder Melky Cabrera (double), and first baseman Adam LaRoche (walk) reached in succession to open the third. Eaton and Cabrera then scored on a two-run single by designated hitter Conor Gillaspie. Shortstop Alexei Ramirez followed with a run-scoring groundout, taking advantage of a poor decision by Astros right fielder George Springer, whose late throw home on the Gillaspie single enabled Ramirez to advance to third base.

The Astros were guilty of several baserunning blunders throughout the series, with shortstop Jonathan Villar adding a key one in the finale.

With Houston trailing 4-0, Villar opened the fifth inning with a triple to straightaway center field. However, Villar attempted to score on the play, following the advice of third-base coach Gary Pettis. Ramirez nailed Villar with a relay throw.

White Sox shortstop Carlos Sanchez added an RBI single in the sixth inning before LaRoche drilled his sixth home run the opposite way to left field off Astros right-hander Jake Buchanan in the seventh.

"We threw out some runners, got some double plays in some big defensive spots to save some runs," LaRoche said. "It was good. We hit the ball with runners in scoring position and pushed some runs across. We just need to be more consistent with that."

Hernandez (2-4) allowed five runs (four earned) on eight hits and one walk with two strikeouts before departing with two outs in the sixth.

Villar committed a throwing error in the sixth, allowing Ramirez to reach. Ramirez scored the fifth Chicago run on the Sanchez base hit.

"I talked to Villar on the bench, I talked to Villar after the game," Astros manager A.J. Hinch said. "We talk about good th