HOUSTON -- Before leaving for a seven-game trip last on July 18, the Miami Marlins had won just once in their previous seven games.
What a difference a week made.
It's the first time they've ever swept in Houston and was their first series sweep since beating the Rays in consecutive two-game series from June 2-5.
"It feels good that we were able to come in here and not have a letdown after a great series in Atlanta," Miami manager Mike Redmond said. "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' homer capped a three-run first for the Marlins, and Ozuna padded the lead with his solo shot in the sixth.
"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."
Jacob Turner (4-6) allowed one run and six hits in 5 2/3 innings to win his second start since moving from the bullpen.
"I really just felt like I had to battle all day, didn't have my best stuff," Turner said. "But at the same time made some pitches when I needed to, got out of jams and that was huge."
Steve Cishek allowed one run in the ninth before getting his 26th save in 29 chances.
Houston's Collin McHugh (4-9), back from a disabled list stint caused by a finger blister, made his first start since July 6 and gave up four runs and seven hits 6 1/3 innings with nine strikeouts for his sixth straight loss.
"When you start talking ... (records) for a starting pitcher, a lot of things have to go right," manager Bo Porter said. "You can pitch well and still not factor into the decision. We've got to score runs. That's pretty much the difference in the game."
Altuve homered and singled twice for his second straight three-hit game and 18th this year. He leads the major leagues with a .344 average and 148 hits, and he also swiped his AL-best 42nd base.
Miami's Giancarlo Stanton struck out four times and has fanned in six straight at-bats.
Christian Yelich hit a leadoff single and scored on a triple by Jordany Valdespin, who came home on Casey McGehee's sacrifice fly. Jones made it 3-0 with his 11th homer, a drive about five rows into the eight-field stands.
Altuve's second leadoff homer of the season and third of his career cut the lead to 3-1 in the bottom half.
Ozuna extended the lead to 4-1 with a sixth-inning homer into the Crawford Boxes in left.
Singleton's ninth-inning homer off Cishek was his first since July 7 and stopped an 0 for 11 skid.
"It's been a while since I hit a ball hard," said Singleton, who is hitting just .178. "It's always nice when you can hit a ball like. Hopefully we can pick up some momentum from what happened (Sunday).
RHP Mark Appel, the No. 1 overall pick in the 2013 amateur draft, has been promoted to Double-A Corpus Christi from Class A Lancaster, where he was 2-5 with a 9.74 ERA in 12 starts. ... The Astros recalled RHP Paul Clemens from Triple-A Oklahoma City before the game. ... Brett Oberholtzer is scheduled to pitch for Houston on Monday, when the Astros open a three-game series with Oakland. ... The Marlins return home to start a three-game series against Washington with Nathan Eovaldi pitching.