In the sense that "a force is best confronted with a force of the same nature", we might say in English
we will hoist him with his own petard
meaning we plan on employing the methods he himself uses in order to "beat him at his own game", an expression which itself could be considered a response to the OP's request.
The expression is much more commonly given as "he was hoisted by his own petard", meaning someone undone by their own plans or actions, without the interference of others, but it can be, and often is, used in the sense of the OP as deliberately employing the particular methods or strategies of another person to defeat them.
Michigan AFL-CIO President Mark Gaffney said his union will remind voters often between now and the November election that McCain supports national right-to-work measures; voted for free-trade agreements that have sent jobs abroad; and promotes a health care plan that would tax benefits. "Our best approach is going to be his record, which is quite anti-worker, anti-middle class, anti-union," Gaffney said. "We will hoist him on his own petard," Gaffney said.
Another example, another, and another.
It is a particularly English expression because it is derived from Shakespeare's Hamlet and thus has found its way into far fewer languages than the Bible.
As an unrelated note, other commenters and answers have mentioned "set a thief to catch a thief". I agree with this, but at least in American English I have almost always heard this as "it takes a thief to catch a thief" which I think is less about 'this is what we are going to do' and more about 'this is what one would need to do; this is how the world works', and so is closer to what the OP is requesting.