Ken Griffey Jr. hit his 606th homer, a two-run shot that allowed the Reds to take a 4-3 lead into the ninth. Cordero (4-3) then gave up a lead for the second time in his last three appearances.
Brian Giles tied it with a run-scoring groundout, and Kouzmanoff broke it open by working Cordero to a full count, then lining a double over the head of Jay Bruce in right field for a 6-4 lead. Cordero retired only two of seven batters, throwing 40 pitches.
Clay Hensley (1-0) pitched two hitless innings for the win. Trevor Hoffman provided drama by allowing the Reds to load the bases with no outs in the ninth. He struck out David Ross, retired pinch-hitter Javier Valentin on a foul pop, then struck out Bruce for his 18th save in 21 chances.
It was a rare comeback by the Padres, who had been 0-53 when trailing after eight innings,
Until Cordero failed for the sixth time in 26 save chances, the Reds were in position to win because of Griffey's homer and another solid start by 22-year-old Homer Bailey.
Griffey snapped a 2-all tie in the sixth with a two-run homer off Josh Banks, who learned the hard way that a marginal mistake can turn into a home run at Great American Ball Park. Edwin Encarnacion had a solo shot off Banks, who had never pitched at the homer-prone park.
Griffey's 13th homer of the season left him three behind Sammy Sosa for fifth place on the career list.
Bailey gave up Adrian Gonzalez's RBI double and Kouzmanoff's sacrifice fly during a 25-pitch first inning, then settled down. The Padres didn't score again until Scott Hairston hit a solo homer off Bailey in the seventh.
Pinch-hitter Chase Headley took a called third strike from David Weathers with a runner on third base, ending the Padres' eighth inning in customary fashion - not quite enough to pull off the comeback. An inning later, they finally did it.
The Padres stranded five runners in scoring position in the first eight innings. They loaded the bases with one out in the fifth and failed to score.
Bruce had a run-scoring double that tied it at 2 in the third and extended his hitting streak to 10 games, the longest of his rookie season.
Notes: Padres SS Khalil Greene was back in the starting lineup after missing a game because of tightness in his lower back. ... RHP Brett Tomko threw in the bullpen on Monday. Tomko has been sidelined all month by a sore elbow. "We'll see how he is tomorrow and determine his fate, whether he throws another bullpen or a simulated game," Padres manager Bud Black said. ... Padres LHP Shawn Estes expects to have the splint removed from his broken left thumb on Friday. He could begin throwing again a few days later. ... Banks is the 388th pitcher Griffey has homered off.