Both players had shown signs of breaking out lately, and they led the Diamondbacks to a breakthrough performance Sunday.
Ryan Zimmerman pushed his hitting streak to 28 games with a double and two singles, and Adam Dunn and Josh Willingham both homered twice. But that wasn't enough to extend the Nationals' season-best three-game winning streak.
Snyder, the Diamondbacks' catcher, gave Hinch the game ball.
"Granted, it's been great to get a first win as a manager," Hinch said, "but honestly, this team needed it and I'm happy for everybody in there."
Arizona's Justin Upton had three hits, including a double, to run his hitting streak to 17 games, second only to Zimmerman's in the majors this season. Ryan Roberts also had three hits, knocking in two runs, as Arizona snapped a three-game slide, the last two under Hinch after Bob Melvin was fired.
"It felt great, being able to push runs across the plate," said Upton, who has raised his average to .309 after a difficult start. "Just continuing to hit, not giving up when we fell behind a couple of times."
The Diamondbacks, who entered with a major league-worst .226 batting average, had six players with at least two hits.
Despite a flicker of success recently, Byrnes was hitting .177 and Snyder .207 entering Sunday's game.
"The guys that are struggling, we're still south of 100 at-bats, most of us," Snyder said. "You sink in, get a little feel, if something goes right, feel good about it, find something that you've been tinkering with, and there you go."
Washington's offense kept churning, but the pitching let the Nationals down.
"Anytime you score over six runs, you should be able to win the ballgame," manager Manny Acta said.
The lead changed hands six times in the first six innings, with Arizona going up for good 8-6 on Snyder's two-out, two-run double in a four-run sixth. Roberts followed with an RBI single to make it 9-6.
Arizona's Max Scherzer failed to get his first victory in 13 major league starts. He left leading 5-4 after Byrnes' two-run homer in the fifth but the Nationals regained the lead in the sixth 6-5 on Zimmerman's' RBI single off reliever Esmerling Vasquez.
Vasquez (1-1) got the win despite giving up two runs in one inning. Chad Qualls gave up a leadoff homer to Willingham in the ninth, then a single to Willie Harris before retiring three in a row for his eighth save in nine chances.
Logan Kensing (0-2), whose ERA skyrocketed to 12.00, allowed four runs in two-thirds of an inning. He just pitched from behind too often, Acta said.
"It doesn't matter how hard you throw up here in the big leagues," Acta said. "If they know a fastball is coming, they're going to hit it."
Dunn, who bats cleanup just behind Zimmerman, had four home runs in the series to increase his season total to 11.
"Zimmerman is more than locked in right now," Snyder said, "and Dunn is a big old donkey."
Zimmerman's hitting streak is the longest by a 3B since Boston's Wade Boggs hit in 28 straight in 1985. ... Arizona will call up 22-year-old Bryan Augenstein from Double-A Mobile to start in place of injured Yusmeiro Petit against Cincinnati on Wednesday. Augenstein was 5-0 in six starts with a 0.78 ERA at Mobile. ... Washington C Jesus Flores sat out after taking a foul ball off his right shoulder in Saturday night's 2-1 victory. ... Arizona's 10 runs matched a season high.