Shairon Martis improved to 4-0 and the Nationals spoiled Hinch's debut with a 5-4 victory over the Diamondbacks on Friday night.
"We're starting to build some confidence and playing a lot better baseball," Washington's Ryan Zimmerman said.
The Nationals, who started the season 1-10, have two road victories in a row for the first time this season and have won four of five overall.
"Sooner or later things had to turn around a little bit," Washington manager Manny Acta said. "We had a rough April and May's been good so far, but there's still a ways to go."
Jesus Flores drove in two runs with a homer and an RBI single, Cristian Guzman tripled in two runs and Adam Dunn homered for the Nationals.
Zimmerman hit safely in the 26th consecutive game, the longest active streak in the majors, when he singled in the first inning.
"I don't really think about it at all," Zimmerman said of the streak. "I've gone farther than I thought I would go. I just enjoy playing and trying to keep the same mindset that I've kept every day and be consistent. So far it's worked."
Hinch, director of player personnel for Arizona, moved into the manager's job after Bob Melvin was fired Thursday night. The new manager said he liked his team's attitude, despite the loss.
"I was proud of the guys for battling back and kind of answering the bell," Hinch said. "Obviously we left a lot of guys on base, had some opportunities which you always reflect on, but the effort was there. I felt like the intensity was high."
Felipe Lopez had three hits, including a double, and scored twice for the Diamondbacks, who erased most of a three-run deficit but lost for the fifth time in six games.
"It was a tough day," Lopez said, "but everybody was focused on winning a ballgame."
Martis (4-0), coming off a complete game triumph over St. Louis, gave up three runs on nine hits in 5 1-3 innings to get the victory. After struggling the previous night in Los Angeles against the Dodgers, Kip Wells pitched a perfect ninth for his first career save.
Yusmeiro Petit (0-3) gave up four runs on six hits in four innings to take the loss.
Phillies 10, Braves 6
At Philadelphia, Cole Hamels pitched six impressive innings to earn his first win since the World Series for the Phillies.
Jayson Werth, Chris Coste and Chase Utley homered for the NL East leaders, who snapped a two-game losing streak.
Making his first start since spraining his left ankle on April 28, Hamels (1-2) allowed two runs, three hits and struck out seven, and lowered his ERA to 6.17.
Atlanta's Casey Kotchman hit a three-run homer off Brad Lidge in the ninth, and Omar Infante also went deep.
Jo-Jo Reyes (0-2) lost his ninth straight.
Mets 7, Pirates 3
At New York, Carlos Delgado hit a three-run homer in a five-run eighth inning and finished with five RBIs, helping the surging Mets to their fifth straight win.
Jonathon Niese plugged a hole in New York's rotation with six effective innings and Carlos Beltran had a tiebreaking RBI single for the Mets, who improved to 3-0 on their eight-game homestand.
Nyjer Morgan had two hits and reached base five times for the slumping Pirates, who have lost six straight and 10 of 11 overall.
Jose Reyes got the winning rally started with a single off Tyler Yates (0-2). Bobby Parnell (1-0) struck out two in a perfect eighth to earn the win.
Astros 2, Padres 0
At Houston, Wandy Rodriguez threw eight sharp innings and Hunter Pence hit a two-run single in the fifth.
In his longest outing of the season, Rodriguez (3-2) allowed five hits without issuing a walk. He struck out seven and lowered his ERA to 1.80, third-best in the league.
Chad Gaudin (0-2) went seven innings and allowed two runs on five hits for the Padres.