The only person that comes to mind who was saved without having to do 'good works' was the criminal who was crucified with him and believed in Jesus despite seeing him in that sorry disposition (crucified, filled with open wounds etc.) therefore making his belief genuine.
Luke 23: 38-43
38There was a written notice above him, which read: this is the king of the Jews.
39One of the criminals who hung there hurled insults at him: “Aren’t you the Christ? Save yourself and us!”
40But the other criminal rebuked him. “Don’t you fear God,” he said, “since you are under the same sentence?
41We are punished justly, for we are getting what our deeds deserve. But this man has done nothing wrong.”
42Then he said, “Jesus, remember me when you come into your kingdom.”
43Jesus answered him, “I tell you the truth, today you will be with me in paradise.”
If you truly have faith in Jesus you will do what he taught for you to do.
Luke 6:46-49
46“Why do you call me, ‘Lord, Lord,’ and do not do what I say?
47I will show you what he is like who comes to me and hears my words and puts them into practice.
48He is like a man building a house, who dug down deep and laid the foundation on rock. When a flood came, the torrent struck that house but could not shake it, because it was well built.
49But the one who hears my words and does not put them into practice is like a man who built a house on the ground without a foundation. The moment the torrent struck that house, it collapsed and its destruction was complete.”