Incredibly, Schell's feat happened in the space of just 22 second-half minutes on Saturday afternoon on a day of spectacular individual feats, with Scotland's Francesca McGhie and Australia's Desiree Miller also scoring hat-tricks.
Canada, second in the World Rugby rankings, had already scored four first-half tries, giving them a healthy lead, before Schell's super-show began with scores in the 50th, 52nd, 54th, 61st, 69th, and 71st minutes completely stealing the show.
Her double hat-trick, though, was not a record. Portia Woodman scored eight for New Zealand against Hong Kong in 2017. It was, however, the second-biggest tally in a single match, tying the half-dozen by American Krista McFarren against Sweden in 1994.
Earlier, McGhie's treble led Scotland's 38-8 demolition of Wales in their make-or-break opener.
Both Six Nations sides were under immense pressure to win. In their pool, both are expected to beat Fiji but neither should trouble Canada, leaving the result of their match likely to decide the second quarter-finalist from the pool.
The all-British contest at Salford had a frantic, desperate air, but Scotland pulled away in the second half to win by a record 30-point margin over their British rivals and are now set to reach the last-eight for the first time since 1998.
McGhie went over after just 54 seconds, only for Wales No.8 Alex Callender to level, but once the Scottish winger went over again in the 17th minute, they never trailed again.
Scotland's build-up was overshadowed by a contracts dispute with the union but they were focussed from the kickoff, eventually running in six tries, with Leia Brebner-Holden, Evie Gallagher and Emma Orr grabbing the others.
In the early game, Australia racked up 11 tries, three from winger Desiree Miller in the first half, as they beat outclassed but courageous Samoa 73-0.
