Kurt Suzuki hit a three-run homer that finished Harvey (2-1), who allowed six runs in 4 1/3 innings and tied a career high with five walks.
Syndergaard was scratched because of right biceps discomfort. While the right-hander hopes to pitch Sunday at Washington, Cespedes looks likely to be sidelined for an extended period.
Cespedes left last Thursday's loss to Philadelphia with a left hamstring problem and returned to the lineup Wednesday. The slugger hit a one-hop double to right-center off R.A. Dickey (2-2) in the fourth and was jogging into second base when he pulled up. When he reached second, he bent over, hands on both knees.