Pospisil set the tone for a close match in a hard-fought first set, which Isner eventually claimed with a late break of serve.
Isner was unable to cement that advantage as both men stayed strong on serve throughout the second set, forcing a tie-breaker as the American failed to convert two break points.
Needing to claim the tie breaker to stay alive, Pospisil rose to the challenge, punishing Isner errors to take the match into a deciding set.
After requiring treatment on his right leg Isner came out fighting in the third set, quickly breaking to build a 3-0 lead in the decider.
With the backing of a vocal Montreal crowd Pospisil once again rallied, breaking back before serving successfully to stay in the match at 5-6 in the final set.
After well over two hours a deciding tie-breaker was needed to determine who booked a place in the second round.
With the pressure on, Isner was visibly tired and the qualifier took advantage to claim a famous scalp 5-7 7-6(5) 7-6(4).
Isner's defeat means that for the first time in ATP Tour history there will be no American player inside the top 20 when ranking points are updated next week.