Read Acts 10, the full account of Cornelius. This is a turning point in the work of the apostles. Verse 2 says Cornelius was a devout and God fearing man before he met Peter. He was saved before he called for Peter but he needed instruction in how Christians are supposed to live. He didn't know the details about Christ. He did know about Christ, though. Go down to v32 and 33. Both verses start with 'you know that...' Cornelius knew about Christ and with his devotion was saved. He was what Paul later referred to as a baby Christian who needed milk but still, he was definitely saved and the Spirit could have come on him at any time.
However, God was holding off with the Spirit until Peter was there. This was a lesson for Peter more than for Cornelius. Peter needed instruction in how to deal with Gentile converts. He'd just experienced his vision with sheet full of unclean thing but didn't know how to apply it. Now Peter fully understood. This was God's lesson to him that Gentiles could be saved and Spirit filled just like the Jews. After this lesson, Peter's attitude and actions changed completely. He was now ready to go out among the Gentiles and to accept Paul's calling as being from the Lord.
The Case of Cornelius is an interesting study. Dr. Luke actually discusses the "full account" in Acts 10, 11, and 15.
Acts 10 is what one could call the general account told by Dr. Luke. Acts 11 is the same account, told by Peter, "by order" . . . or one might say he told them what happened in the chronological order of events.
Luke tells us that Cornelius was devout man in the eyes of the Jews, but he was lost.
Look at what Cornelius told Peter when he arrived, with regards to what the angel had said unto him . . .
Acts 11: 14-15
14
Who shall tell thee words, whereby thou and all thy house shall be saved. It was the words that Peter was to deliver that had the power to create saving and obedient faith in Cornelius.
But Peter and the six Jewish Christians of the Circumcision, that accompanied him to the house of Cornelius, need to be convinced that Cornelius was worthy to hear the Gospel. That is why God sent the Holy Spirit directly from heaven, rather than by the laying on of an Apostle's hands (such as Peter and John Acts 8:18)
15
And as I began to speak, the Holy Ghost fell on them, as on us at the beginning...
Since faith comes by hearing the word of God (Rom 10:17) and the Holy Spirit fell on the household of Cornelius before he heard the word, then we can conclude that this miraculous falling of the Spirit had nothing to do with his salvation. The Gospel is the power of God unto salvation (Roman 1:16)
So it is clear, that once the six Jewish brethren and Peter saw that Cornelius and his household had received the Holy Spirit directly from heaven, as had he and the other Apostles (Acts 2:1-4) they were convinced the Gentiles were accepted by God (Acts 11:16-18; 15:7-9) and received salvation through faith and obedience to the Gospel command to be baptized (Acts 10:47-48)
