Chris Young hit a solo homer for the A's, who are 10-0 against their new AL West foes this season and 15-1 all-time. The Astros have lost six straight overall.
Houston took an early 3-0 lead thanks in part to Oakland tying a season high with three errors. Young's shot cut the lead to one in the seventh before Reddick's drive to right field off Wesley Wright (0-4) made it 4-3.
Young also tripled for another big game in his hometown.
Three of Young's nine homers this season have come at Minute Maid Park, and he's hit eight home runs with 30 RBIs in 22 career games in Houston.
Ryan Cook (3-2) pitched a perfect seventh for the win and Grant Balfour did the same in the ninth for his 26th save. Balfour has converted his last 44 chances dating to last season, an Oakland record.
Chris Carter drove in a run for Houston and shortstop Jonathan Villar singled, scored and had a stolen base in his major league debut.
Oakland starter Tommy Milone allowed five hits and three runs — two earned — in six innings.
Dallas Keuchel yielded five hits and a run with five strikeouts in six innings for Houston.
Justin Maxwell doubled to start the Houston second and stole second base. Maxwell scored and J.D. Martinez reached on an error by shortstop Jed Lowrie to make it 1-0.
Villar got his first major league hit with a bunt single in the third. Villar, who stole 31 bases in Triple-A this season, quickly swiped second. Carter's single to center scored Villar to extend the lead to 2-0.
Carter scored on an error by second baseman Grant Green when he couldn't make the catch on a routine fly.
Josh Donaldson got to second on a two-base error by Astros third baseman Matt Dominguez in the fourth and advanced to third on a groundout. Keuchel then walked Derek Norris, but retired the next two batters to end the threat.
Keuchel struck out the first two batters of the fifth inning before a triple by Chris Young. He left Young stranded when he fanned Lowrie to end the inning.
Donaldson singled to start the sixth before a double down the right-field line by Nate Freiman. Reddick drew a walk with one out to load the bases, and a sacrifice fly by Green got Oakland within 3-1.
Keuchel escaped the inning when he struck out Seth Smith.
NOTES: The series continues Tuesday when Houston's top pitching prospect, Jarred Cosart (1-0), will be recalled from Triple-A Oklahoma City to make his second major league start against Jarrod Parker (6-6). The 23-year-old Cosart took a no-hitter into the seventh inning and got the win in his debut against Tampa Bay just before the break, allowing two hits and no runs in eight-plus innings. ... Home Run Derby winner Yoenis Cespedes was out for the fourth straight game because of a sore left wrist but is feeling better. Oakland manager Bob Melvin said Cespedes did a lot of work in the cage and will take batting practice Tuesday if he doesn't feel any soreness. Melvin isn't sure if Cespedes could play Tuesday. ... A's LHP Brett Anderson, who has been on the disabled list since May 1 with a stress fracture in his right foot, threw 35 pitches in a bullpen session. "He threw the ball really well," Melvin said. "You could tell he was excited to be out there and he didn't have any issues with his foot." Melvin said Anderson will throw another bullpen session Wednesday.