Romans 6:14 declares: "For sin shall not have dominion over you: for ye are not under the law, but under grace." The Greek word for "dominion" — kyrieusei — means to be lord over, to have mastery over. Paul is asserting that the power of compulsion does not have the final authority over the person in Christ. This is not a promise that the compulsion immediately disappears — Paul spends the rest of Romans 7 describing the ongoing struggle. But it is a statement about ultimate authority: what once had lordship no longer has it.
1 Corinthians 10:13 addresses the specific experience of temptation that feels irresistible: "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." The promise is not that the temptation will be removed. It is that a way of escape will be made available — always. Recovery programs, sober communities, medical support, counselors, and honest accountability are among the practical forms that "way of escape" takes.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.