With Cliff Pennington aboard following a leadoff double, Hinske drove a 1-2 pitch from John Axford (0-1) onto the concourse beyond the wall in center field.
Hinske raised his right arm as he rounded second with his eighth pinch-hit homer -- and definitely one of his longest shots of his career.
"It was a hanging breaking ball and I put a good swing on it and it just kept going," Hinske said. "That kind of surprised me too, how far I hit it. It felt great. I didn't even feel it hit the bat."
Hinske, a Wisconsin native, had his brother and some of his college buddies in the stands.
"They were all jacked up. I pointed at them after I crossed home plate," Hinske said. "So that was cool. My uncle was here. My mom and dad actually left today . . . but I had a voicemail from them."
Tony Sipp (1-0) struck out two in a perfect 10th inning and Heath Bell held on for his first save after J.J. Putz blew an opportunity in the ninth.
Jonathan Lucroy had a one-out RBI single that left runners on the corners, but Rickie Weeks and pinch hitter
Kyle Lohse -- a starting pitcher forced into duty after manager Ron Roenicke ran through his available players -- struck out to end the game.
"Heath threw the ball really good at the end," Arizona manager Kirk Gibson said. "I mean they got some hits off him, but we moved and they hit them in the hole. The hardest hit ball was the first out of the inning."
Ryan Braun stepped into the on-deck circle with Weeks at the plate, but Roenicke called him back into the dugout after he struck out.
"He couldn't hit," Roenicke said. "We were up there so if it came down to it they would have to figure out if he could hit or not. Make a decision to maybe walk Rickie or not."
Aaron Hill also had a two-run homer as Arizona earned its fourth consecutive win and improved to 5-1 for the third time in franchise history. The Diamondbacks also won five of their first six games in 2000 and 2012.
Milwaukee has dropped five in a row since it beat Colorado 5-4 in 10 innings on opening day. Yovani Gallardo was hit hard again, yielding four runs and nine hits in six innings, but remained unbeaten in eight career starts against Arizona.
The Brewers played without Braun, who is out with a neck injury, and shortstop
Jean Segura was pulled before the fifth inning due to a bruised left quad. Third baseman Aramis Ramirez went on the disabled list on Saturday with a sprained left knee, and first baseman Corey Hart is expected to miss the first month of the season recovering from right knee surgery.
Segura was injured when Gerardo Parra made a hard slide into his leg to break up a potential double play in the third inning. Segura tried to stay in the game, earning a loud cheer from the Miller Park crowd, but was replaced in the field before Arizona batted in the fifth.
"Just a muscle thing," Segura said. "I don't think it will take too long. Hopefully we will see tomorrow."
The Diamondbacks carried a 6-4 lead into the ninth, but the Brewers jumped all over Putz to send the game to extra innings. It was the first blown save of the season for the closer.
Pinch hitter Josh Prince started the rally with his first career hit, a long drive to center for a leadoff double. Norichika Aoki then singled to right on the next pitch, giving him three RBI on his bobblehead day.
Aoki swiped second and scampered home on Lucroy's one-out single, delighting the Miller Park crowd of 37,733. The Brewers had a chance to end the game right there, but Lucroy was stranded when Weeks and Alex Gonzalez struck out to end the inning.
Aoki had a career-high four hits and Gonzalez belted a solo homer in the fourth, but it wasn't enough as the Brewers once again struggled to contain
Paul Goldschmidt and Hill.
Hill went 3 for 6 and is batting .490 (25 for 51) with three homers and eight RBIs in 12 career games against Milwaukee. Goldschmidt had six hits and five RBI in the series, and is hitting .400 (12 for 30) in eight games against the Brewers.
Notes: If everything goes well, the Diamondbacks think they will get OF Cody Ross back before they open a three-game series against the Los Angeles Dodgers on April 12. Ross is rehabbing a strained left calf. . . . Parra went 1 for 6 and is batting .400 (12 for 30). "He is off to a good start," Gibson said. "It certainly helps him to be playing every day. (Martin) Prado has been a great influence on him. He is happy." . . . RHP Marco Estrada (0-0, 7.20 ERA) gets the ball when Milwaukee opens a three-game series against the Chicago Cubs on Monday. Estrada will be opposed by RHP Edwin Jackson (0-1, 3.60) in the first game of the season at Wrigley Field. . . . Arizona hosts Pittsburgh on Monday in the opener of a three-game set. Diamondbacks RHP Trevor Cahill (0-1, 4.76) is slated to face LHP Wandy Rodriguez (1-0, 0.00).