Ireland's Margaret Johnston, who had led going into the final round of matches, had to settle for silver after being pipped 25-24 by the defending champion, South Africa's Jo Peacock.
Price later admitted she was more at home in team disciplines and said: "I enjoyed the week but I'm not really a great singles fan. I think my game is more suited to team games."
Johnston could not hide her disappointment, saying: "I was trying not to watch what was happening on Mary's rink and concentrating on my own game."
Wales' Betty Morgan took the bronze, edging out Peacock on shots differential after she beat Namibia's Jean Joubert 25-22. Wales took silver behind South Africa in the fours when Kathy Pearce, Sarah Mansbridge, Nina Shipperlee and Rita Jones beat Namibia 29-9 to beat Scotland on shots aggregate.
The Scots rink of Kath Houston, Susan Kelly, Janice Maxwell and Sarah Gourlay had to settle for bronze after beating Israel 24-13. Wales captured the overall team title, finishing on 50 points ahead of England on 45.