After Peter had preached the gospel to the Gentiles, Jews in Jerusalem criticized him for going to Cornelius’ house. In defense of his actions, Peter said: “Then the Spirit told me to go with them (those who came from Cornelius), doubting nothing  Moreover these six brethren accompanied me, and we entered the man’s house. And he told us how he had seen an angel standing in his  house, who said to him, Send men to Joppa, and call for Simon whose surname is Peter, who will tell you “words by which you and all your household will be saved” (Acts 11:12-14).

Cornelius was a good man, but that did not save him (Acts 10:1,2). He had an unusual experience, but that did not save him (Acts 10:3). He even received Holy Spirit baptism, but that did not save him (Acts 10:44-47). Peter said this showed that the Gentiles could be saved (Acts 11:15-18).

How was he saved? Cornelius said that Peter told him “words by which you and your household will be saved” (Acts 11:14). The gospel is God’s power unto salvation (Rom. 1:16). What did Cornelius do? He obeyed the words Peter taught him (read Acts 10:47,48; Acts 2:38).