Quentin battled Phillies reliever Francisco Rosario to a 1-2 count before just getting his bat on a slider that he was able to hook toward the shortstop hole just out of the reach of Rollins.
"He had a pretty good slider, and he was rushing it up there pretty good," Quentin said of Rosario. "I got some good wood on it and got it by Rollins. I was a little scared there. It made it through, so I was happy that happened."
The win was the second straight for the D-backs, who had lost their previous five games.
Arizona starter Doug Davis held the Phillies scoreless through six innings before tiring in the seventh, as he allowed two runs that tied the game, 2-2.
"I had trouble with my curveball early, but I still had my fastball and my cutter so I worked with those," said Davis, who threw 112 pitches before leaving with one in, two on and no one out in the seventh.
The D-backs retook a 3-2 lead in the bottom of the seventh when pinch-hitter Chad Tracy lifted a sacrifice fly to center. It was the first at-bat for Tracy since injuring his ribcage last Tuesday in Los Angeles.
Tracy was down 1-2 during the at-bat before fouling off a pitch and eventually running the count to 3-2 before driving in the run.
"He didn't try to do too much," D-backs manager Bob Melvin said.
Melvin then turned things over to setup man Brandon Lyon, who retired the first two batters in the eighth before giving up back-to-back doubles to Aaron Rowand and Wes Helms to tie the game again.
The D-backs had one more rally left in them, as Byrnes drew a one-out walk against Rosario, moved to third on Stephen Drew's single to right and scored when Quentin singled.
Quentin is one of the D-backs' young hitters who has struggled through the first six weeks of the season, but he's now driven in the go-ahead run in each of the last two games. He credited the work of hitting coach Kevin Seitzer, as well as the words Melvin spoke during a pregame meeting Sunday when he told the young players he still had faith in them and that he wanted them to believe in and trust their talent.
"The coaching staff has been awesome as far as keeping us positive and picking us up and talking us through things and giving us their experiences," Quentin said. "They have a lot of faith in us, and it feels good when someone has faith in you. It gives you more confidence. I think they've been doing all they can with us and they're doing a great job."
"It's coming," Melvin said of the offense.
It didn't come quick enough to get Davis a win, but the defense did its part. Chris Young, who was 3-for-4 with a pair of doubles at the plate, made two outstanding catches in center. The first was a sliding catch on a Rollins bloop to lead off the game, while the other was a leaping grab at the wall of Pat Burrell's drive in the sixth.
"I just try to keep it a close game, keep it within a swing of the bat or two," Davis said. "They're going to come around, and they did tonight late in the game with clutch hits. I wouldn't have been out there for the seventh if it hadn't been for great defense behind me."
"I feel bad he didn't get the win," catcher Miguel Montero said. "But that's baseball. He was outstanding, just outstanding."