From that city many of the Samaritans believed in Him because of the word of the woman who testified, "He told me all the things that I have done." So when the Samaritans came to Jesus, they were asking Him to stay with them; and He stayed there two days. Many more believed because of His work; and they were saying to the woman, "It is no longer because of what you said that we believe, for we have heard for ourselves and know that this One is indeed the Savior of the world." John 4:39-42, NASB
The woman was an unlikely evangelist. But then she had an exceptional message to match her exceptional (spelled "notorious" here) life. She had met a man, she announced to the villagers, who had told her everything that she had ever done. That had their ears. Because what she had done was much, and everybody knew it. As a result of her testimony, the center of the village shifted toward the well with the woman in the forefront.
We read in The Desire of Ages that "as soon as she had found the Saviour the Samaritan woman brought others to Him. She proved herself a more effective missionary than His own disciples. The disciples saw nothing in Samaria to indicate that it was an encouraging field. Their thoughts were fixed upon a great work to be done in the future. They did not see that right around them was a harvest to be gathered. But through the woman whom they despised, a whole cityful were brought to hear the Saviour. She carried the light at once to her own countrymen.
This woman represents the working of a practical faith in Christ. Every true disciple is born into the kingdom of God as a missionary. He who drinks of the living water becomes a fountain of life. The receiver becomes a giver. The grace of Christ in the soul is like a spring in the desert, welling up to refresh all, and making those who are ready to perish eager to drink of the water of life" (p. 195).
The woman of Samaria might have been an unlikely evangelist, but she was a successful one. She had a message about her sin and her Savior that led others to investigate for themselves. In the process, they also found a personal Savior.
Before Jesus came into the woman's life both she and her neighbors considered her beyond hope. But Jesus performed two miracles in her life: He enabled her to break away from her past, and He opened up to her a new future.
From that perspective, there is nothing else that Jesus can be called but "Saviour of the world."