Since the only way New Testament believers are sanctified was "with might by His Spirit in the inner man (Eph 3:16)" it follows that believers in the Old Testament were sanctified in the same way.

Since justification is (and always has been) by faith which is the gift of God by which Christ dwells in our hearts (Eph 3:17), why would it be different under the Old Testament? We look back in time with faith to the Cross, while the Old Testament saints looked forward with faith to the Cross. But the faith itself, the gospel, the God Who justisfies and sanctifies both groups has always done so by faith. Indeed neither saving faith nor sanctification is possible except by the Spirit's indwelling presence.