The game started with Adam Eaton ripping a double to left-center field against Reds starter Mike Leake. With two outs, Dunn scorched Leake's first pitch off the glove of third baseman Chris Nelson for an RBI single.
Leake was making his delayed spring debut and pitched two innings, allowing one run and two hits with one strikeout. He was pushed back because of a minor abdomen strain but showed no ill effects.
"They were aggressive, so it made it tough to get into a count with them," Leake said. "The one Dunner hit was a good pitch. He's a hitter that likes to jump on that first pitch. I'm not worried about that stuff on the first outing."
Cincinnati took a 2-1 lead in the bottom of the first inning against White Sox starter Felipe Paulino. Zack Cozart lined a one-out double off the wall in right-center field. Two batters later, Bruce crushed a 1-1 pitch well over the fence in right field.
With two outs in the Reds' second inning, Roger Bernadina smoked a double through the gap in left-center field and scored on Nelson's lined single to left field.
Paulino gave up three runs on four hits over three innings, with one walk and five strikeouts.
"It's Spring Training," Paulino said. "I felt like I threw the right pitch, but [Bruce] got me there. It was down and away ... he just made a good swing. It's baseball. I just tried to make pitches, and he got me that time. But I got him the second time [on a groundout]. It's about competing, and next time we'll compete again."
In the third inning, Alex Liddi's two-out RBI single off of the Reds' Aroldis Chapman tied the game.
Chicago scored two runs against Reds reliever Tim Crabbe in the fifth. Gordon Beckham lined an RBI single to center field and, with two outs, Dunn overcame a shift with a sharply lined RBI single past diving second baseman Skip Schumaker.
Up next: Closer candidate Nate Jones is set to make his first Cactus League appearance Saturday after battling a moderately strained left glute since the start of White Sox camp. Veteran lefty reliever Scott Downs also is set to make his White Sox debut. Jose Quintana opens the game against the D-backs with a 2:05 p.m. CT first pitch, making his second Cactus League start for a game to be carried live on Gameday Audio.