The D-backs snapped out of their collective offensive funk, collecting 17 hits as they outlasted the Nationals, 10-8, in front of 25,086 at Chase Field.
The win snapped a three-game losing streak for Arizona and ended Washington's three-game winning streak.
"It's great to get a first win as a manager, but honestly, this team needed it," said Hinch, who lost his first two games since taking over for Bob Melvin last week. "And I'm happy for everybody in there."
After going 3-for-26 with runners in scoring position during Hinch's first two games, the offense bounced back to pick up eight hits in 21 such at-bats on Sunday.
"I think one of the strengths of this team can be the length of our lineup," Hinch said. "We have enough guys that obviously can help turn the lineup over and over and grind through some at-bats. When we're good, that happens."
The 17 hits were a season high, and the 10 runs matched the team's best output of the year.
"Hopefully, this is the start of us being a productive offense," said Mark Reynolds, who went 2-for-5 with a pair of runs scored. "It wasn't relief. We thought we had a good matchup, and we expected to win, and we did."
The D-backs trailed on three separate occasions. They were down 2-1 in the third, 4-3 in the fifth and 6-5 in the sixth.
Each time, though, they found a way to battle back, first off Nats starter Scott Olsen and later against Washington's struggling bullpen.
"We answered back multiple times during this game," Hinch said. "The guys never quit, never got down, kept upbeat."
The D-backs took the lead for good with a four-run rally in the bottom of the sixth off reliever Logan Kensing.
One of the runs scored on a fluke play, when Chris Young was hit in the back with a throw at third and wound up scoring when the ball bounced away from Ryan Zimmerman.
One out later, Chris Snyder ripped a double to right to score two runs to break the tie and give Arizona an 8-6 lead. Ryan Roberts, who had three hits and two RBIs in a rare start, drove in the final run with a single to center.
"It was just a good game," Snyder said. "It's something to build on, and hopefully, it's something that can continue."
Even with a 9-6 lead, the game was far from over.
The Nationals pushed across a run in the seventh to cut the lead to two runs, but the D-backs added a run in the eighth on Roberts' sac fly.
"That was a huge at-bat there," Snyder said of Roberts' RBI. "That was a big run."
The D-backs turned the game over to closer Chad Qualls in the ninth, and after allowing a leadoff homer to Josh Willingham -- his second of the game -- as well as a single to Willie Harris, Qualls was able to retire the next three hitters to finally bring the game to a close.
"It was crazy," Snyder said of the game, which lasted three hours and 52 minutes. "It was a long game. It was, wow. But we battled. We kept hitting. They would score, we would answer, they scored again, we answered."
As he congratulated Qualls after the final out, Snyder asked him if he would mind if he gave the ball to Hinch, and Qualls told him to go ahead.
Scherzer, who allowed four runs over five innings, is now winless in his 22 big league games, 13 of which have been starts. The Nats made him work hard and ran his pitch count up early.
"They fouled off a lot of pitches," Scherzer said. "I was throwing strikes, but give credit to them -- they made me work hard today. I'm just happy the team won, that's the most important thing."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.