Corbin (1-0) gave up a run in each of the first two innings, but settled in to win his season debut, giving up two runs on eight hits and one walk with two strikeouts in six innings.
"I was a little off, having eight days off coming in and I was a little excited," Corbin said. "Left some balls up early."
The Brewers led, 2-1, with runners on second and third in the second inning, but Corbin got Rickie Weeks to ground out to end the threat. With the game still close, Arizona scored three runs in the third off Milwaukee's Mike Fiers (0-1) to go ahead for good.
"Corbin keeping them to one run in the second was a great job by him, and obviously our pitchers shut them out the last seven innings," Goldschmidt said.
Kubel's two-run homer gave the Diamondbacks a 3-2 lead in the fourth. Goldschmidt then hit a two-run drive in the fourth to make it 6-2. Hill's solo shot capped the scoring in the eighth after his RBI double in the first gave Arizona a 1-0 lead.
Arizona had 16 hits with seven starters getting two hits apiece.
"We hit the ball out of the ballpark today, got some big blows and kept the pressure on them," Arizona manager Kirk Gibson said. "Got contributions from everybody, so overall, a good day for us."
The start was another in a disturbing trend for Fiers, who struggled at the end of 2012 and in spring training. He gave up six runs on nine hits and a walk while striking out one in five innings of his season debut.
"Commanding the baseball is the main problem," Milwaukee manager Ron Roenicke said.
He said Fiers' problems could be caused by fatigue, lack of confidence or simply being out of rhythm.
"We need to find out what the answer is and get him on the right track," Roenicke said.
Milwaukee was playing without star Ryan Braun, who missed his second consecutive game with neck spasms, and cleanup hitter Aramis Ramirez, placed on the 15-day disabled list Saturday with a sprained knee.
Jean Segura had two singles and a double for Milwaukee, which has lost four consecutive games after beating Colorado on opening day. The Brewers had 10 hits, but went 1 for 7 with runners in scoring position.
"He got in trouble, but cut it off and got back on track," Gibson said of Corbin. "That's a good start for us."
Besides missing Braun and Ramirez, Milwaukee slugger Corey Hart is expected to be out the first month of the season recovering from right knee surgery. The slew of injuries left journeyman infielder Alex Gonzalez to bat cleanup Saturday night with Yuniesky Betancourt playing first and batting sixth.
With Milwaukee leading 2-1, Goldschmidt doubled off the left field wall to open the fourth. Kubel hit the next pitch from Fiers into the right field stands for his first homer of the year to give the Diamondbacks the lead for good, 3-2. Arizona scored another run in the inning to make it 4-2 on singles by Eric Chavez, Cliff Pennington and Gerardo Parra.
Arizona stretched the lead to 6-2 in the fifth when Miguel Montero walked and Goldschmidt hit a 1-1 pitch from Fiers into the left field bleachers for his second homer. Fiers finished the inning, but was replaced to start the sixth after throwing 97 pitches.
After going 6-4 with a 1.80 ERA in his first 13 appearances last year as a rookie, Fiers struggled in his last 10 starts of 2012, going 3-6 with a 6.99 ERA. In spring training, he had a 6.98 ERA in 19 1/3 innings.
Pitching for the first time since starting against Cincinnati in spring training on March 29, Corbin allowed a sacrifice fly to Gonzalez in the first and an RBI double to Segura in the second as the Brewers opened a 2-1 lead. He then threw four scoreless innings, departing after six innings.
OF Cody Ross went 0 for 3 Saturday night in a rehab start for High-A Visalia. Ross is on the DL with a strained left calf and is 0 for 8 in three games as the DH. ... INF-OF Josh Prince was recalled from Triple-A Nashville to take Ramirez's place on the roster. He entered the game in the seventh and flied out in both of his at-bats. ... Brewers LF Khris Davis doubled for his first major league hit in the second. ... A pitch by LHP Michael Gonzalez that had been ruled a wild pitch Friday night was changed by the official scorer on Saturday to a passed ball by C Jonathan Lucroy. Two runners scored on the decisive play in Arizona's 3-1 victory.