Dunn returned to the White Sox this week after attending the Academy Awards ceremony in California last weekend. He had a nonspeaking role in the Oscar-nominated "Dallas Buyers Club."
Dunn's first single came off Mike Leake, who was making his first spring start. Dunn later broke a 3-all tie in the fifth.
"Jay's was a blast," acting manager Jay Bell said. "It is fun to see his timing. His timing is really good right now and we have three weeks left. Jay is going to be fun to watch this summer."
Aroldis Chapman pitched two innings for the Reds, allowing a run and two hits. He struck out three.
Paulino is trying for a spot in the White Sox rotation. He allowed three runs but struck out five in three innings, finishing strong.
"Everybody is competing for a spot," White Sox manager Robin Ventura said. "You can just hand one to somebody. I think everybody understands where they're at but you still have to come down here and earn a spot in the rotation."
Reds: Leake was scratched from his first start when he felt an abdominal strain that first occurred during his offseason workout. He threw 27 pitches and felt no discomfort in his two innings of work.
He gave up one run and two hits and struck out one.
"The strain was weird," Leake said. "If it was the regular season I would have pitched through it. You can't base anything off two innings, you don't go deep in counts or face batters twice. At some point this spring I'll push through an extra inning, but it didn't make sense the first time out."
White Sox: Paulino missed all of 2013 while recovering from surgery on his right elbow. He was limited to seven rehabilitation starts last season in the Kansas City organization.
"It feels good to be back on the mound. Things will come together soon," he said. "I missed some spots, mechanically. Bruce hit a pitch down and away. That's going to happen."
Paulino gave up four runs on eight hits in 1 2/3 innings in his first spring start but had no lingering effects or soreness between starts.
"I am feeling great. I like how I recovered over the last four days," Paulino said.
White Sox: Reliever Nate Jones, a candidate for the closer's job, threw 45 pitches on Wednesday. He expects to make his first spring appearance against Arizona on Saturday. ... Right-hander Matt Lindstrom has been shut down for a few days. He felt some discomfort during a throwing session on the sidelines on Wednesday.
Reds: Right-handed reliever Jonathan Broxton is scheduled to throw another bullpen on Saturday. He threw 30 pitches in a bullpen session on Wednesday. ... Left-handed pitcher David Holmberg is bothered by a sore right ankle. ... Jack Hannahan continues to take batting practice but has not appeared in a game. He had surgery on his right shoulder after last season. ... Mat Latos had elbow surgery in October and left knee surgery on Feb. 14. He threw 25 pitches in a bullpen session on Wednesday and is scheduled for another on Saturday. ... Left-hander Sean Marshall has a sore left shoulder.
Adam Eaton doubled, walked and scored two runs against the Reds. He is trying to win the leadoff spot in the order. Eaton has six hits in 10 at-bats in five games.
Reds catcher Brayan Pena walked to lead off the fourth inning. The Cuban native has two career stolen bases, but has been caught four times.
White Sox pitcher David Purcey ignored him and he took off for second. The attempt was delayed and second baseman Gordon Beckham and shortstop Alexei Ramirez failed to cover the bag, letting catcher Tyler Flowers' throw go into center field as Pena advanced to third.