Fister (8-3) gave up two runs on four hits and struck out five.
"If I can work at a good pace, that allows our defense -- our guys that are really good -- to stay on their toes and get into the dugout to go back to hitting, and that's what they do well," Fister said. "It is an all-around great effort, and it allows me to stick with the sinker and attack the zone."
The Astros have won Fister's last 10 starts, and in those games, Fister has gone at least 5 2/3 innings and allowed three runs or fewer.
"We play good when he pitches and he sets the tempo," manager A.J. Hinch said. "It starts with the starting pitcher. We do a good job behind him. He continues to pound the strike zone."
Fister's winning streak ties for the longest of his career, which he set Aug. 20-Sept. 26, 2011, and it is the second longest in the AL behind Baltimore's Chris Tillman with nine.
Houston's offense has at least five runs in seven of Fister's past 10 starts.
"It's a jumpstarter not only for me but for the whole team," Fister said. "For me, I still take the mindset, it's a 0-0 ballgame, and it doesn't affect the way I'm attacking hitters or change the game plan at all. We stayed with what we thought would work, and I thought it worked well tonight."
Altuve hit a monstrous 431-foot solo homer to center in the fourth to give the Astros a 7-0 lead. Castro led off the seventh with a solo home run.
"We are doing all the small things to get on base and score," Altuve said. "Fister was the key to the game today. He threw really good today."
Correa launched a two-run shot in the sixth and finished with three RBI.
Houston has won five of its last six games. It took advantage of starter Jhoulys Chacin's wildness in the first and third to score three runs in each inning.
Chacin (2-3) allowed six runs -- five earned -- on six hits and walked a season-high five in a career-low two innings. After throwing a complete game against Detroit on May 30, Chacin has allowed three runs or more in his last four starts and has only pitched into the sixth in one of those outings.
"He was just missing," Angels manager Mike Scioscia said. "Definitely had problems getting pitches into the zones he wanted to."
Angels: RHP Nick Tropeano (right shoulder soreness) is likely to start a rehab assignment this week. ... 2B Cliff Pennington (strained left hamstring) is rehabbing in Arizona this week. ... C Geovany Soto (right knee) was evaluated after a workout Sunday and could begin a rehab assignment this week. ... RHP Joe Smith (strained left hamstring) threw off a mound Sunday and has played catch three straight days.
Angels: LHP Hector Santiago (4-4) will look for his second straight strong start Tuesday against the Astros after throwing six innings and allowing one run in a win against Minnesota in his last start. Santiago is 1-0 with a 1.85 ERA in four starts against Houston.
Astros: RHP Collin McHugh (5-5) will also be looking for his second straight solid outing after tossing 6 2/3 innings and allowing one run in his last start, a no-decision.
- Home Plate Umpire - Ramon DeJesus
- First Base Umpire - Gary Cederstrom
- Second Base Umpire - Eric Cooper
- Third Base Umpire - Adrian Johnson