The White Sox hadn't swept a four-game series at Fenway Park since 1927.
Xander Bogaerts made sure the streak will live on another year.
Bogaerts' single to center field off rookie reliever Matt Purke in the 10th inning gave the Red Sox an 8-7 victory Thursday afternoon.
Right-hander James Shields turned in his first decent outing since joining the White Sox via trade from the Padres on June 4, but the bullpen coughed up five runs.
After being swept by the Indians last weekend in Cleveland, the Sox finished the trip 3-4, and their mood after the game danced between frustrated over the missed opportunities Thursday and happy about winning three of four at Fenway.