"It meant a lot that I could contribute to the victory," Barrero said through an interpreter. "I felt better today. I still have to work on a couple things. I'm working on cutting down on my swing and try to hit it up the middle."
"I didn't really think about my last home run when I went to the plate," Aquino said. "I just enjoyed the game and the process and do my best."
It was the Reds' highest scoring game since an 8-2 victory over Baltimore on July 30.
"To come in that spot and not give up any runs is huge," Reds manager David Bell said. "You expect that he will give up a run and we still hold the lead, but to completely shut it down against those two hitters is really special. I think for any pitcher to get five outs to end the game is special. He looked really comfortable, not that it was easy."
Five Reds relievers combined for 5 1/3 scoreless innings.
Cincinnati's Joey Votto made his 1,989th career appearance, snapping a tie with Hall of Famer Larry Walker for the most in major league history by players born in Canada.
The teams combined for four homers and 10 runs in the first four innings.
Patrick Wisdom gave the Cubs a 2-0 lead with a two-run drive that squeezed just inside the left-field foul pole in the second. Aquino responded with his fourth homer in the bottom half, a deep drive into the lower deck in left.
Chicago grabbed a 5-4 lead with three runs in the fourth. Yan Gomes hit a tying a two-run shot that reached the first row of the second deck in left. Christopher Morel then went deep on the next pitch.
"We had some quality at-bats," Cubs manager David Ross said. "The back-to-backs were fun."
The Reds tied it in the bottom half with help from a balk called on reliever Anderson Espinoza (0-2).
Cincinnati right-hander Justin Dunn was tagged for five runs and seven hits in 3 2/3 innings in his second start since coming off the injured list. He had been sidelined by a right shoulder strain.
Chicago right-hander Keegan Thompson lasted just 1 2/3 innings. He was charged with four runs and two hits.
"He was getting ahead in the count, 0-2 and 1-2, but he couldn't put them away," Ross said. "They hit a lot of foul balls that turned into walks. He couldn't finish the at-bats."
Reds: OF Nick Senzel left in the fourth with a tight right hamstring. ... RHP Art Warren (right upper arm) was scheduled to make his fourth rehab appearance for Single-A Dayton against Lansing. Warren has been on the 15-day injured list since July 4.
Cubs: RHP Marcus Stroman (3-5, 4.20 ERA), Monday's scheduled starter in Washington, allowed five hits and four runs for a no-decision in his last start, also against the Nationals in Chicago.
Reds: LHP Mike Minor (1-9, 6.24 ERA) hasn't won in nine starts going into Monday's game against Philadelphia in Cincinnati.