The Phillies held a 3-0 lead after six innings but the White Sox scored single runs in the seventh, eighth and ninth innings, forcing a third straight extra-inning contest in their series.
But Utley began a rally by stroking a double against David Purcey (0-1) to lead off the 10th.
After Jimmy Rollins was intentionally walked, the runners advanced on Domonic Brown's groundout and Darin Ruf was also issued an intentional pass to load the bases.
Ramon Tronscoso took the mound and fanned Delmon Young for the second out, but Mayberry then scorched a grounder up the middle, sending Utley home with the game-winner.
Anthony Bastardo (3-2) was credited with the decision as the Phillies took the rubber match of the series and improved to .500 (48-48) for the first time since June 7.