This is definitely a biblical concept, and have heard similar to it I thought. But, when asked to find this by another, I am having little luck.
closed as off-topic by curiousdannii, Lee Woofenden, depperm, KorvinStarmast, Nathaniel♦ May 24 '18 at 12:54
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This seems to be a chapter title from The Recognitions of Clement Book IV:
Chapter XXXIII.—The Weakest Christian More Powerful Than the Strongest Demon.
”Is it, then, that we are of another and a superior nature, and that therefore the demons are afraid of us? Nay, we are of one and the same nature with you, but we differ in religion. But if you will also be like us, we do not grudge it, but rather we exhort you, and wish you to be assured, that when the same faith and religion and innocence of life shall be in you that is in us, you will have equal and the same power and virtue against demons, through God rewarding your faith. For as he who has soldiers under him, although he may be inferior, and they superior to him in strength, yet ‘says to this one, Go, and he goeth; and to another, Come, and he cometh; and to another, Do this, and he doeth it;’ and this he is able to do, not by his own power, but by the fear of Cæsar; so every faithful one commands the demons, although they seem to be much stronger than men, and that not by means of his own power, but by means of the power of God, who has put them in subjection. For even that which we have just spoken of, that Cæsar is held in awe by all soldiers, and in every camp, and in his whole kingdom, though he is but one man, and perhaps feeble in respect of bodily strength, this is not effected but by the power of God, who inspires all with fear, that they may be subject to one.
1 Corinthians 10:13 gives a vague reference to this idea, but is not an exact match.
There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it.
"Resist the devil, and he will flee from you." -- James 4:7
Not close at all in the wording you're looking for, but the principle it conveys lines up.
Personally, I've always found this to be one of the most astonishing and wonderful statements in all of scripture. You resist -- Satan flees. Wow.
These signs shall follow them that believe: In my name they shall cast out devils. (Mark 16:17)