Kansas City had held a 3-2 advantage since the fourth after Johnny Giavotella had driven in a run with an infield single. Boston staged its rally in the seventh, when Mauro Gomez walked to lead off the inning against Bruce Chen and Mike Aviles followed with a single off reliever Kelvin Herrera.
After Scott Podsednik sacrificed the runners along, Ciriaco doubled to left to put the Red Sox ahead and on their way to snapping a four-game losing streak.
Ciriaco scored in the first on a two-run single by David Ortiz, who played for the first time since July 17. He spent time on the disabled list with an Achilles injury.
Herrera (1-2) took the loss, having retired only one batter in the seventh.