The victory in just over two hours put the 33-year-old world number three into the third round as he began his final tune-up tournament for the US Open.
The Swiss great, who had notched his 200th Masters match win against Lleyton Hewitt at Cincinnati five years ago, arrived at the tournament he has won five times off a runner-up finish to Jo-Wilfried Tsonga in Toronto.
He delivered a dominant third set to finally subdue the 46th-ranked Pospisil, who was a finalist last month in Washington. He stretched his career record over the Canadian to 3-0.
But Federer powered through the third, breaking his opponent twice on the way to victory and finishing with 23 winners and 21 unforced errors, with six aces along the way.
While safely followed top seed Novak Djkokovic into the third round, two of the men's top eight were toppled.
Taiwan's Lu Yen-Hsun stunned Czech fourth seed Tomas Berdych 3-6, 6-3, 6-4 while Poland's Jerzy Janowicz upset number seven Grigor Dimitrov 6-4, 3-6, 6-3 -- four days after the Bulgarian played a semi-final in Toronto.
Murray, who lifted the Cincinnati trophy in 2008 and 2011, is searching for his first title since winning Wimbledon 13 months ago.
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