"I think he continues to show good stuff," Indians manager Terry Francona said. "The one inning when they got the runs, we lost a ball in the sun, things like that, and then they hit the ball hard. I think he's making progress. His arm is good. He looks healthy. I think it's exciting. That's the best way to put it."
Brantley got the Indians on the board in the first with his first home run of the spring. The three-run shot came after Lonnie Chisenhall and Nick Swisher each collected two-out singles.
"Nice swing," Francona said. "That's the way you swing at a 3-0 pitch. That was good. We had a good day. We got a bunch of at-bats early."
The D-backs cut the lead to 3-1 in the bottom of the first on Aaron Hill's two-out RBI double.
Arizona starter Ian Kennedy, though, did not appear sharp, allowing back-to-back doubles to start the second as Cleveland went up 4-1.
The D-backs took advantage of a misplay by Brantley in left to tie the game with three runs in the third. Martin Prado drove home two of them with a double, and Eric Chavez added an RBI single.
Omir Santos gave the lead right back to the Indians with an RBI single in the fourth.
Kennedy, who will start Opening Day for the D-backs, allowed five runs on nine hits while fanning seven over five innings.
Up next: Opening Day starter Justin Masterson is scheduled to log seven innings on Friday, when the Indians host the D-backs in a 10:05 p.m. ET Cactus League contest at Goodyear Ballpark. The game will be televised on SportsTimeOhio, and a live webcast will be available on indians.com. Infielder Mike Aviles and catcher Carlos Santana -- back from stints with Puerto Rico and the Dominican Republic, respectively, in the World Baseball Classic -- are slated to return to Cleveland's lineup. Tribe relievers Matt Albers and Rich Hill are also down to pitch.
Steve Gilbert is a reporter for MLB.com. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.