Quintana (3-1) didn't allow a hit until David Ortiz singled with one out in the seventh. The left-hander finished with 6 1/3 shutout innings, yielding three hits and a pair of walks while walking five.
Addison Reed hurled a 1-2-3 ninth for his 16th save as the White Sox clinched their three-game series in Chicago.
Keppinger's blast in the fifth inning broke a scoreless tie and Alex Rios added an RBI double in the eighth for an insurance run.
Boston's Felix Doubront (3-2) absorbed the loss, surrendering two runs on five hits over six full frames.