The Pole, who won one of her six grand slam titles at the US Open in 2022, was in complete control against Shnaider on Monday, combining crisp ball striking with strong court coverage to overwhelm her Russian opponent in 68 minutes.
The win set up a semi-final clash against veteran Elina Svitolina - a 3-6 6-0 6-3 winner over Russia's Ekaterina Alexandrova - who beat Swiatek in the Rome semi-finals in May.
Former world No.1 Swiatek broke twice in the opening set, capitalising on a string of mistakes from Shnaider, who committed 12 unforced errors in the set.
There was little respite for Shnaider in the second set as seventh seed Swiatek continued to dictate play from the baseline and never faced a break point.
The win puts Swiatek into her first WTA 1000 semi-final of an inconsistent season in which she has failed to advance beyond the quarters at a grand slam and suffered a surprise second-round defeat by compatriot Magda Linette in Miami.
That loss led Swiatek to make a coaching change, replacing Wim Fissette with Francisco Roig.
Swiatek was also beaten in straight sets by Alexandra Eala in the third round at Wimbledon, where she was defending champion.
In Monday's later quarter-final, Alexandrova was untouchable in the first set, picking up where she left off after beating world No.1 Aryna Sabalenka in the previous round.
But Ukrainian Svitolina stormed back to level the match in the second set and grabbed a 4-1 lead in the third when she pounced on a net cord and hammered home a backhand for another service break.
Svitolina dropped two games while leading 5-1 but regrouped to break serve and advance.
In Montreal, rain has forced the postponement of the two Canadian Open men's quarter-finals scheduled for Monday.
All four quarter-finals of the Masters 1000 tournament will now take place on Tuesday. Spain's Rafael Jodar and American Ben Shelton are among the quarter-finalists.
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