Rogers, Milwaukee's 32nd-round pick in this year's Draft, fell a triple shy of the cycle. He tied for sixth in the league during the regular season with 32 RBIs, hitting .281 with three homers in 42 games.
Nick Shaw, one of the Brewers' two Arizona League All-Stars, went 4-for-4 with a double, four runs scored and two RBIs. Ken Allison chipped in two hits and scored twice.
Shaw, a 25th-round pick in June, started the decisive rally in the eighth with a two-out single. He took third on a base hit by Kenneth Allison and scored on a wild pitch by relief Jose Marizan (0-1) to snap an 8-8 tie. Allison stole third and came on with an insurance run on Rogers' third hit of the night.
Riding a seven-game winning streak into the one-game Final, the Reds grabbed the early lead. Kurtis Muller hit an RBI triple in the second and fellow AZL All-Star Robert Maddox capped a two-run third with an RBI single.
But the Brewers got on the board in the bottom of the inning on an error by Reds starter Radhames Quezada and tied it on Rogers' two-run double. Back-to-back RBI doubles by Drew Poulk and Juan Silva put the Reds back on top in the fourth, but the Brewers answered with four runs in their half.
Shaw came through with a two-run single and Rogers snapped a 5-5 deadlock with a two-run homer. The 22-year-old first baseman had three homers in 42 regular-season contests.
Both teams scored a run in the sixth, but Maddox homered and Jaren Matthews lifted a sacrifice fly in the seventh to lift the Reds into an 8-8 tie.
Seth Harvey (1-0) got the win after striking out three in 1 2/3 hitless innings. Jose Sanchez pitched around a hit and a walk in the ninth and saved both of the Brewers' playoff wins.