The Reds improved to 37-18 since the All-Star break.
"Our pitching has been great all year, from the first guy to the last guy," said Bruce. "We're resilient. It's the mark of a team that has players who understand their roles. It's a cliche that it takes 25 guys to win a championship. But it's true."
Arroyo (12-7) improved to 8-1 with a 3.03 ERA in his past 10 starts. He threw first-pitch strikes to 18 of the 28 batters he faced on Saturday, making quick work of the young Astros.
"Houston is a really young team, they give you opportunities to get some quick innings," said Arroyo, who was making his 229th start for the Reds, 11th on the club's all-time list. "If you throw the ball in the zone, they swing [for] it. That's ideal for me."
The Astros scored off Arroyo in the first inning on Saturday when Fernando Martinez doubled and scored on Justin Maxwell's bloop single putting them ahead 1-0. Martinez extended his hitting streak to five games.
That is all the offense Houston would muster off Reds pitching.
It was then bombs away for Cincinnati before 35,018 at Great American Ball Park.
Bruce's 421-foot bomb to center tied the score in the second. It was Bruce's 33rd home run this season, a new career-high. He has homered in six of his past eight games.
"Personal goals are nice, and I'll reflect on those when the season is over," said Bruce. "But we have a championship to win."
Phillips' 16th home run, a low liner to right field, put the Reds ahead 2-1 in the third.
"They're a good hitting team," said Astros starter Bud Norris. "I think I really only made one really bad pitch tonight and that was the first solo shot to Bruce. I think Phillips put a great swing on that pitch, and I threw it where I wanted."
Norris (5-12) allowed five earned runs on six hits in 5 1/3 innings.
Arroyo cruised after the first with four strikeouts through three innings.
Defense helped Arroyo's cause. Houston had runners on first and second in the fourth and sixth innings, but each time the Reds turned double plays to end the inning.
"That's Bronson," said Reds manager Dusty Baker. "When he gets locked in, he can go on a roll."
Joey Votto singled to left in his first at-bat on Saturday, reaching base for the seventh time in his first nine plate appearances since coming off the DL. Votto went 2-for-3 with a double and a run scored.
Henry Rodriguez recorded his first Major League hit with a pinch-hit single in the eighth.
Votto began the sixth with a ground-rule double to right-center. After Bruce was intentionally walked with one out, Todd Frazier walked to load the bases. Ryan Hanigan singled to drive home Votto making the score 3-1.
On the 10th pitch of his at-bat against Fernando Rodriguez, Wilson Valdez hit a slow roller to the left of the mound. Rodriguez slipped as he fielded the ball then threw past catcher Jason Castro. Two runs scored, giving the Reds a 5-1 lead.
Houston, which has scored three or fewer runs in 13 of Norris' 17 outings, was unable to generate any rallies. The Astros had runners on first and third in the ninth when Jonathan Broxton struck out Jimmy Paredes to preserve the win.
So, the Reds edged closer to the postseason on Saturday night behind the reliable Arroyo, who discussed his performance afterwards. Sans ice.
"I've just been a guy that needs regular work," Arroyo said. "Too many days off makes me feel weak. I have a strange body like that. I need to be in the weight room doing stuff. Later in the season, I can dial up. I generally feel good down the stretch."