What Paul means in this passage becomes clear when we understand the sense and usage of two Greek words, those translated as “win” and “save.” In the evangelical world, both of them have taken on lives of their own, but with just a little digging, we will see that no contradiction lies between this passage and the numerous other clear statements.
The word translated as “win” is kerdaino (Strong's #2770), and its basic meaning is “gain,” which is how it is typically translated. It means “to acquire by effort or investment.” It can mean “to earn” or “to make a profit.” The flipside is that it can also mean “to cause a loss not to occur.”
This word is used infrequently, but the verses that contain it are well known. For example, Jesus uses it when He cautions against gaining the whole world yet losing one's own soul (Matthew 16:26; Mark 8:36; Luke 9:27). The gain is a physical or material one—it is not speaking of evangelizing the whole world. It also appears in the Parable of the Talents, where two of the servants gain more talents through their efforts and investments (Matthew 25:16-22).
Kerdaino is also found in the well-known Matthew 18:15, where Jesus says, “If your brother sins against you, go and tell him his fault between you and him alone. If he hears you, you have gained your brother.” The gaining here is not about “winning” someone “for Christ.” When we gain our brother, we are gaining a better relationship. We are keeping a breach in the relationship from continuing. We receive a profit, as it were, by enhancing theconnection or bond between us. There is no implication that we are opening his mind to the mysteries of God's Kingdom. It simply means that after bringing a sin to his attention, if he hears and receives us, then we have gained our brother because the relationship has been restored.