The Reds scored four in the second on five hits, including a three-run home run from Ivan De Jesus Jr. De Jesus finished a triple short of the cycle.
But the White Sox broke free for six in the fourth to claim a 7-4 lead. Adam Eaton singled home two, while Jimmy Rollins and Hector Sanchez each delivered an RBI single. Jason Coats walked with the bases loaded to force home another run.
That advantage didn't last long, as Adam Duvall lofted a three-run homer to left in the fifth to forge a tie. Rodon was lifted by manager Robin Ventura after De Jesus singled and Jordan Pacheco walked, with the Reds eventually scoring five in the frame, two on Billy Hamilton's double.
Todd Frazier knocked two hits for the White Sox playing against his former club, adding a run scored.
Finnegan allowed seven runs (six earned) over 3 1/3 innings, giving up six hits and four walks. He struck out six.
Rodon yielded 10 hits and nine earned runs in 4 1/3 innings, striking out three and walking two.
Sanchez replaced Alex Avila in the top of the fourth, with Avila leaving due to lower back stiffness. Avila is day to day.
Up next for White Sox:Mat Latos makes his second Cactus League start, in a rematch from Tuesday against the Giants and starter Jake Peavy. The game begins at 3:05 p.m. CT in Scottsdale.
Up next for Reds: Cincinnati has a 4:05 p.m. ET game Sunday against the Dodgers at Camelback Ranch. Alfredo Simon gets his second start of the spring. Simon has been the Reds' best starter since signing as a free agent on March 17, pitching three innings of shutout, no-hit ball and striking out four on Tuesday vs. the Cubs.