Schmitt had a team-high 16 spikes from 21 attempts to guide Canada to a historic 3-0 (25-22, 34-32, 25-23) triumph to shell shock the Olympic champions.
Nicholas Hoag was also instrumental with 15 points, while Stephen Timothy Marr (9 points) made a slew of clutch plays late in the third set to help Canada produce the boil over.
Brazil was uncharacteristically ragged as evidenced by opposite striker Wallace De Souza who scored a game-high 19 points through flashes of brilliance but also made some key errors.
It was just the fifth time Canada has beaten Brazil at the world level from 27 attempts and ended a run of eight straight defeats. Canada have improved their record to 6-4, while it was a costly defeat for Brazil who lost for just the second time in the VNL after coming into the fourth phase tied on eight wins with Poland.
Despite being the overwhelming underdog, Canada matched their highly-rated opponents from the get go with little separating the teams during a tense first set. Canada constantly repelled repeated attacks from Brazil and then made their move late in the set with clutch serving from Hoag giving his team a mini-break at 22-19.
Brazil peeled off three straight points as it appeared order had been restored but a tenacious Canada had other ideas as a thunderous spike from Schmitt regained their lead and they won the next two points to clinch the opening set in a sign of things to come.
Overcoming their first set wobble, Brazil came out firing in the second stanza and led 14-8 as it appeared they would level the contest but Canada fought back impressively to ensure the set went the distance.
Both teams had numerous chances to claim the second set with a thumping spike from Canada reserve Arthur Szwarc saving a set point during a pulsating stretch.
Wallace was keeping Brazil in the contest with tenacious play marked by desperate lunges but both teams made crucial mistakes during the pressurised passage. There were a slew of clutch plays highlighted by a beautiful setup from Brazil leading to a sizzling strike from a leaping Lucas Saatkamp to save a fifth set point as fans were on the edge of their seats.
It appeared Canada would be unable to close it out with Schmitt making a service error on their sixth set point but it was followed up by a service gaffe from Brazil as the swirling anticipation was proving too much for the players. On their eighth set point, Canada finally prevailed through a Wallace error to gain a stranglehold over the contest.
Facing a monumental upset, Brazil came out determined in the third set and stormed out to a 10-6 lead but the memories of letting slip the second set returned with Canada coming back into the contest levelling the scores at 14 apiece. The standard lifted and peaked during a mega rally filled with spectacular hustle from Canada but ultimately won by Brazil to gain a 16-14 lead at the second technical timeout.
Canada kept fighting but were unable to get ahead as a thumping shot put away by Wallace put Brazil ahead but that was countered by a thunderbolt from Graham Vigrass as the match continued to follow a tense path. Points continued to be traded with Canada's blocking at the net thwarting Brazil's vaunted artillery with Szwarc particularly impressive.
A well worked set led to a put away from Marr to give Canada a 24-23 lead and within sight of a memorable victory, which they wrapped up moments later through an ace from a jump-serving Tyler Sanders to trigger wild celebrations from his players.
Canada plays hosts Bulgaria on Saturday, while Brazil will be looking to bounce back from the shock result in a blockbuster match against powerhouse France.