HOUSTON -- Miami Marlins manager Mike Redmond adhered to the familiar cliche of taking things one game at a time almost as a mechanism to offset just how exceptionally his team performed over the past week.

First baseman Garrett Jones and center fielder Marcell Ozuna slugged solo home runs to power the Marlins to a 4-2 victory over the Houston Astros and an interleague series sweep on Sunday at Minute Maid Park.

The Marlins (51-53) completed their seven-game road trip through Atlanta and Houston 6-1 and improved to 7-3 since the All-Star break. Miami is 11-4 in interleague games, tops in the National League, and recorded its first sweep of the Astros (42-63) in Houston in club history.

"It is hard to believe," Redmond said of the series sweep. "I remember back in the day this was not an easy place to play: (Craig) Biggio, (Jeff) Bagwell, (Lance) Berkman and all those guys, and their pitching.

"It feels good that we were able to come in here and not have a letdown after a great series in Atlanta. I think that's probably the biggest thing. We did what we needed to do to win and that's a good feeling out there right now."

Jones' blast to right field in the first inning, his 11th, capped the Marlins' three-run frame against Astros right-hander Collin McHugh (4-9). With one out in the sixth, Ozuna drilled a hanging slider 411 feet into the left-field seats for his 16th home run, snapping a four-inning span during which McHugh reclaimed his rhythm and kept Miami in check.

McHugh struck out nine over 6 1/3 innings, but his rocky first frame proved costly. Before Jones took him deep, McHugh surrendered a leadoff single to left fielder Christian Yelich before right fielder Jordany Valdespin followed with a run-scoring triple into the right-field corner.

"You never want to give the other team the early lead like that," McHugh said. "As a starter, I pride myself on giving my team a shutdown inning to start the game so they can come up to bat with a fresh slate. Today was not exactly how you want to draw it up."

The early run support proved beneficial for Marlins right-hander Jacob Turner (4-6), whose effectiveness with men on base confounded the Astros (42-63). Turner surrendered a leadoff home run to Astros second baseman Jose Altuve in the first inning, but that was his lone blemish.

Leadoff batters reached base safely in the third, fourth and fifth innings for the Astros against Turner yet were left stranded on each occasion. The Astros finished 0-for-8 with runners in scoring position.

Altuve went 3-for-4 and stroked leadoff base hits in the first, third and fifth innings. He was left stranded in scoring position after stealing second base in the third, and was erased as part of an inning-ending double play off the bat of Astros left fielder Chris Carter in the fifth.

Astros first baseman Jon Singleton belted a solo home run, his seventh this season, off Marlins closer Steve Cishek with one out in the ninth. Cishek recovered to strike out catcher Carlos Corporan and right fielder Robbie Grossman in succession to record his 26th save on the season.

"You have to score runs," Astros manager Bo Porter said. "Right now, we're just not getting the big hit. Altuve continues to swing the bat well, but we need some other guys to get it going."

Miami last swept Houston July 7-10, 2011, during a four-game series. With the Nationals and Reds visiting Miami this week, the Marlins are aiming for a postseason push should they maintain this momentum.

"It was huge to get this last win and head home, and confidence is high," Jones said. "We've got the Nationals coming in so it's going to be a big next few games. It was good to have a good road trip and just take that confidence going back home and continue playing good baseball."

NOTES: The Astros promoted top pitching prospect Mark Appel, the No. 1 overall pick in the 2013 draft, to Double-A Corpus Christi despite the fact that Appel (2-5, 9.74 ERA) struggled mightily with high Class A Lancaster. Appel threw a bullpen session at Minute Maid Park on Sunday while en route to Corpus Christi. ... Before recording a three-run double that put Miami ahead to stay on Saturday, Marlins DH Giancarlo Stanton had produced just 20 of his 66 RBIs on the road, his 30.3 road percentage ranking as the second-lowest among players with at least 50 RBIs (Rockies OF Charlie Blackmon, 30.2 percent). ... Astros LHP Brett Oberholtzer will start the series opener against the Oakland A's on Monday, having supplanted RHP Brad Peacock in the rotation. Oberholtzer has been solid as the Astros' "sixth" starter, effectively filling in as an injury replacement.