play into the hands

play (right/straight) into sb's hands and play (right/straight) into the hands of sb (to do what someone you are competing with wants you to do, without realizing it; to do exactly what an enemy, opponent, etc. wants so that they gain the advantage in a particular situation) — играть на руку кому-либо ; подыгрывать; ~ лить воду на чью-л. мельницу

...play into the hands of the enemy/opponents/etc — играть на руку врагу / противнику

Example 1: If we respond with violence, we'll be playing into their hands, giving them an excuse for a fight. (LDOCE)

Example 2: If we get the police involved, we'll be playing right into the protesters' hands. (OALD)