"Anytime you [allow] a six-run inning, it's difficult to come back from," manager A.J. Hinch said. "But what do we do? We come back and get four and make it a game."
Mike Fiers labored into the sixth inning, allowing four runs, and the Astros' bullpen gave up another four in the frame, putting Houston down 8-2.
But the team with 35 come-from-behind wins in 2015 nearly added another behind the three late-inning home runs.
"It's great to see," Fiers said. "This team never thinks we're out of a game."
Following Oakland's six-run outburst, Villar unloaded on a 1-0 fastball from A's starter Felix Doubront in the seventh, sending it into the second deck down the left-field line.
Later in the inning, with runners on first and second, Correa obliterated a 3-2 fastball off Fernando Rodriguez into the bleachers in left-center to pull the Astros within two. The rookie's 17th home run was projected by Statcast™ to land 434 feet from home plate -- the second longest of his career -- and left his bat at 112 mph.
"Since day one, I really noticed we have a power lineup, from the leadoff guy until the guy hitting in the nine-hole," Correa said. "We know we've got guys that can drive the ball out of the ballpark."
When A's catcher Josh Phegley responded with a two-run bomb, the Astros' offense didn't recoil.
Villar, in the eighth, drove in a run with a grounder and Marisnick launched a two-run homer.
The Astros may not win every game down the stretch, but at least Hinch knows his club will give him all it has every time out.
"We compete until the end," Hinch said. "There's not a doubt in my mind what we're going to do. You see it in our guys. There are a lot of reasons why we're a good team and one of them is because we play until the end."
Oliver Macklin is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.