Jesus taught that through him comes our purification (i.e. righteousness), and it is as a result of this righteousness that we obtain eternal life.
• E.g. Jn 11:25 — “I am the resurrection and the life; he who believes in Me [thereby being purified] will live even if he dies,” cf. Jn 6:35, 8:12)
• E.g. Jn 20:31 — that believing you may have life in His name.
• E.g. Matthew 25:46 — These will go away into eternal punishment, but the righteous into eternal life.”
• Jesus accepted baptism by John the Baptist, and the gospels say John taught it. (see below)
Paul taught that through a mysterious union between the believer and Jesus Christ—wherein the believer would be counted righteous—the believer would be raised from death while non-believers would remain in their sins and therefore not enjoy eternal life.
• Romans 6:4 — Therefore we have been buried with Him through baptism into death, so that as Christ was raised...
• Romans 8:11 — But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ...
• 1 Corinthians 6:14 — Now God has not only raised the Lord, but will also raise us up through His power.