One-shot deviation principle for infinite repeated games and dynamic programming In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming.

Because, in repeated games, a one-shot deviation refers to one history, so on equilibrium path, a one-shot deviation could produce a play that differs on more than one stages from the original equilibrium path.

Is it true for the sequence of state variables and control variables in dynamic programming? In other words, can a one-shot deviation generate an aforementioned sequence that differs for more than one stage?
A deviation (one-shot or not) can certainly generate a sequence that differs from the optimal one for an arbitrary number of periods. 

You could treat a dynamic programming problem as a repeated game between one player and chance. The one-shot deviation principle should then carry over from repeated games to dynamic programming.