In the 4 Gospels, Jesus tells several people that if you have faith, you or family member or friend will be healed, or have already been healed because of your faith. In John 3:16, he says those who believe in the Son will have everlasting life.
But I don't think there’s a place in the Gospels in which Jesus says his death in particular will take away each person’s sin. Which Paul made an absolute centrality in his letters.