Trailing 4-2 in the fifth inning, Ciriaco began Boston's comeback with a solo homer and newly acquired James Loney provided a two-out RBI single later in the frame to forge a tie score.
The Bosox took the lead for good in the sixth when Jacoby Ellsbury singled home Mauro Gomez and Ciriaco added another run-producing hit in the seventh as the Red Sox went on to win the third contest in their four-game series.
Dustin Pedroia contributed a solo homer for the Bosox.
The rally made a winner of Pedro Beato (1-0), who was making his first appearance for Boston since being acquired from the New York Mets this month.
Kansas City starter Will Smith (4-6) was tagged for five runs (four earned) on nine hits over five full innings.
Lorenzo Cain socked a three-run homer and Tony Abreu supplied two run-scoring singles for the Royals.