Cordero posted his 321st career save, tying him with Jose Mesa for the all- time record by Dominican-born relievers.
"He's climbing up the list," Reds manager Dusty Baker said. "Certainly it would have been terrible had we lost that game."
Dave Sappelt posted three hits and scored twice for the Reds, who dropped the opener on Monday by a 4-3 count.
Bryan LaHair's pinch-hit two-run homer in the bottom of the ninth was the lone offense for the Cubs, who saw their two-game win streak snapped.
John Grabow (3-1) was charged in the setback with two runs and four hits over two relief innings.
Cincinnati failed to produce a run with the bases loaded in the first, but starter Mike Leake kept the Cubs at bay. He faced the minimum through five innings, with the lone hit allowed erased on a double play.
"He was attacking the bottom of the strike zone. He doesn't mess around," Cubs manager Mike Quade said of Leake.
The Reds snapped the scoreless deadlock in the sixth. Sappelt led off with a single and scored when Votto doubled to right. Jay Bruce singled to put runners on the corners and a Devin Mesoraco grounder plated another run.
Cincy's starter retired the side in order in the sixth, then worked around a catcher's interference call on Mesoraco which put a man on in the seventh. He hit Alfonso Soriano to start the eighth, but Marlon Byrd hit into a double play and Tyler Colvin flied out.
Leake entered the ninth with a two-run lead and a chance to record his first career shutout, but Starlin Castro managed to reach on a slow roller to short with two down and moved to second on defensive indifference. LaHair ensured extra innings when he launched a shot over the right field bleachers.
The Cubs had the bases loaded with one out in the 10th, but Jeff Baker hit into a rare, but inning-ending, 5-2-3 double play. Chicago also stranded two in the 11th.
Leake wound up with two runs and three hits with six strikeouts over nine innings...Cubs starter Rodrigo Lopez exited after 5 2/3 innings, yielding eight hits and a pair of runs...Castro has reached base safely in 20 straight games, becoming the first Chicago shortstop to do so since Ryan Theriot reached base in 28 straight back in 2007...Prior to the game, the Cubs recalled pitcher John Gaub, infielder DJ LeMahieu and outfielder Lou Montanez from Triple-A Iowa.