Heisey hit his second and third homers of spring training and drove in four runs. Phillips hit his first homer and drove in three while scoring three.
Billy Hamilton stole two bases, giving him four in Cactus League play for the Reds.
Reds starter Brett Marshall threw three shutout innings, working around four hits and three walks while striking out four.
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.
Aroldis Chapman pitched two innings for the Reds, allowing a run and two hits. He struck out three.
Alfredo Simon starts for the Reds versus the Cubs on Saturday afternoon. Coverage begins at 2 35pm on 700 WLW.