Jones scored two in the eighth and final end of play for a 6-5 win when Sherry Middaugh's last rock hit a guard and the two rinks shook hands. Jones had blanked the seventh end to retain last rock heading home.
Jones had surrendered three to Middaugh's Coldwater, Ontario curlers in the sixth end to fall behind.
Jones and her Winnipeg crew will meet Sweden's Margaretha Sigfridsson who scored an 8-4 tirumph over reigning world champion Binia Feltscher's rink from Switzerland.
Ottawa's Rachel Homan continued to advance towards a third consecutive masters title, with an 8-3 over Switzerland's Silvana Trrinzoni.
Homan's crew will meet Edmoton's Val Sweeting, 5-2 winners over Switzerland's Alina Paetz.
Competition continues at Selkirk Recreational Centre with the men contesting their quarter-final round.