Arroyo, who earned his first winning decision since May 7 and just his third of the year, is now 8-2 with a 2.90 ERA in his career against the Mets.
"At this point in the season, having two wins, I'll take a win any way I can get it," he said. "If I gave up 15 and we score 16, I'll take it. I was happy with my performance."
Arroyo, who leads the National League in starts and innings pitched since he was acquired prior to the 2006 season, struck out five and did not allow a run until the sixth, but he was hurt by two late home runs.
"He had better velocity tonight," Reds manager Dusty Baker said of Arroyo. "He was 88-89 [mph] and that's 3-4 mph faster than he had been throwing, and that sets up his breaking stuff. He had real good command of all his pitches."
Mets starter Dillon Gee also went six innings, allowing four runs -- three earned -- on five hits while striking out four.
Bruce's home run -- the Reds' first inside-the-park homer of the season and the first since Drew Stubbs' on June 17, 2011 -- carried into the left-field corner and just out of the sliding reach of Jason Bay in the second. Bay exited the game after the play, with a likely concussion. The next hitter, Todd Frazier, singled and then came around to score on a Ryan Ludwick double.
Gee hit Joey Votto in the third inning before Phillips launched his ninth homer of the year -- on the ninth pitch of his at-bat -- over the left-center-field fence for a 4-0 Cincinnati advantage.
"It was just a lack of execution on the changeup," Gee said. "I threw him a changeup and it just came right back over the middle of the plate, and he did what he does."
What Phillips has been doing the last 18 games is providing the Reds with power out of the cleanup spot -- and protection for Votto. Phillips has 22 RBIs in those contests, and he has now homered in a career-best three consecutive games.
"I motivate myself regardless of where I'm hitting," Phillips said. "I want to go out there and do my job the best I can and try to help the team win. That's my motivation in itself. Regardless of who I'm hitting behind or in front of, I have to go out and do my job. I'm the four-hitter. I have to drive in runs."
Since moving into the cleanup spot on April 18, the second baseman is hitting .301 with eight homers and 40 RBIs.
"He's coming up big time," Baker said. "He's got 40 RBIs now, and he's been our hottest hitter outside of Joey Votto the last month. He had a bad [hamstring], then he had a bad hand. You don't win a [Silver Slugger Award] because you can't hit. ... He's batted first, second, cleanup, and I'm very satisfied. You look at his production the last couple weeks, and it's a direct correlation between us winning and what he's doing in that spot."
The Mets didn't get to Arroyo until the sixth, when Kirk Nieuwenhuis led off the inning with a homer to deep right field. Scott Hairston, who entered for Bay, also went yard off Arroyo -- a two-run shot in the seventh -- to cut the Reds' lead to 6-3 after Cincinnati scored twice in the top half of that frame.
"I did pretty much what I wanted with their lineup," Arroyo said. "I gave up two homers -- one on a hanging breaking ball and one on a pretty good pitch that was up and in. That's the way it goes. We had a comfortable lead, and those two extra runs were huge."
Cincinnati tacked on one more in the top of the ninth, and the Reds' bullpen -- Jose Arredondo, Sean Marshall and Aroldis Chapman combined for three innings of spotless ball -- closed it out.
"It starts with one [win], and we're at four and hope to take it to five," Baker said.