Maddux, who attacked a cooler with his bat last week in Miami, tied Hall of Famers Don Sutton and Nolan Ryan for 13th place on the all-time victory list while pitching the Cubs to their second straight triumph.
Maddux had been one victory away from catching Sutton and Ryan the entire month. He came into the start with an 0-4 record and 7.81 earned-run average in May after going 5-0 with a 1.35 ERA in April.
Despite sitting through an hourlong rain delay, Maddux allowed only three runs on seven hits in a 64-pitch performance, leaving with two outs in the sixth inning after incurring stiffness in his legs and back.
"Just kind of sticking," he said. "I wasn't sliding."
Maddux blamed it on the rain delay and warming up twice, downplaying the injury.
Jacque Jones' home run and four RBIs sparked the offense as the Cubs won two games in a row for only the second time since April 26.
"I'm starting to have fun again," Jones said. "I'm starting to enjoy playing the game and not trying to impress people and worry about things I can't control."
What changed things?
"Nothing," Jones replied. "I figured I couldn't get any worse than what I was doing. I could only go up from there. I made some mistakes, and I acknowledged them. I'll never run away from them. We all make mistakes. I'm just trying to stay positive and keep a positive outlook. It hasn't been pretty for our team. It hasn't been pretty for me at some points in the season, but we just have to keep going."
Cincinnati, which now has lost five of its last six games, took a 1-0 lead in the second inning on Adam Dunn's leadoff double and Edwin Encarnacion's sharp single to right. Jones' throw to the plate sailed high and wide, hitting the protective screen on the fly over a leaping Maddux, allowing Encarnacion to advance to second base.
But Jones made up for his error in the fourth with a three-run double off Brandon Claussen after Claussen walked the first two men he faced following a 61-minute rain delay. An RBI single by Henry Blanco, who was mired in an 0-for-21 slump over his previous eight games, raised the lead to three runs, and the Cubs never trailed again.
Leading 7-3 in the eighth, Jones homered off another left-hander, ex-Cub Kent Mercker.
"That's when I play my best," Jones said. "When I have a smile on my face."
The Cubs improved to 7-21 in May, a disastrous month that finally comes to a close Wednesday when Carlos Zambrano tries to lead the Cubs to their first series sweep since they beat St. Louis three straight in the opening home series of the season.