Cristian Guzman tripled in two runs and Adam Dunn homered for the Nationals, who have won two in a row on the road for the first time this season.
Washington's Ryan Zimmerman hit safely in the 26th consecutive game, the longest active streak in the majors, when he singled in the first inning.
Hinch, director of player personnel for Arizona, moved into the manager's job after Bob Melvin was fired Thursday night.
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.
Shairon Martis (4-0), coming off a complete game, gave up three runs on nine hits in 5 1-3 innings to get the victory. 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.
Lopez led off the first with a double, advanced to third when Young fouled out, then scored on Justin Upton's ground out. The Nationals took the lead on a two-out, two-run triple by Guzman over Upton's head in right field in the second.
Solo homers by Dunn in the third and Flores in the fourth made it 4-1.
The Diamondbacks cut it to 4-2 when Young - coming off a 1-for-19 road trip
- tripled in Lopez from first with no outs. But Young was stranded on third when Upton and Mark Reynolds struck out, then Josh Whitesell lined out to right.
Arizona was hitless in 36 tries with runners in scoring position before Josh Wilson singled to put runners at first and the third in the sixth. Pinch hitter Eric Byrnes then snapped an 0-for-17 skid with an RBI single up the middle to cut the lead to 5-3.
