Chicago right fielder David DeJesus misplayed a fly ball by Phillips that should have been the third out of the inning, leading to the run that moved the Reds closer to the National League Central title.
Any combination of Cincinnati wins or St. Louis losses totaling three during the remainder of the season will make the Reds division champions.
Phillips reached second base on the error by DeJesus and then scored on a single to left by Stubbs.
Chicago had rallied from a four-run deficit to force extra innings.
Joey Votto doubled home a run in the first and singled in two more during the third to help the Reds build a 5-1 lead.
Alfonso Soriano hit a two-run homer for the Cubs as part of their comeback and they tied it in the eighth when Welington Castillo drew a bases-loaded walk.
Chicago put runners on second and third in the 10th inning without scoring. Logan Ondrusek (5-2), who worked out of trouble in that inning, eventually became the winning pitcher. Jonathan Broxton turned in a perfect 11th for his 27th save.
The unearned run in the 11th was surrendered by Alberto Cabrera (0-1), who suffered his first major-league loss in his 21st relief appearance.