Pospisil, ranked 129th in the world, triumphed 6-4, 7-6 (7/5), sealing the biggest win of his career on his fourth match point to the delight a stadium court crowd won over by the underdog's aggressive serve-and-volley style.
For Britain's Murray, it was yet another disappointing performance in the California desert, where his best showing is a 2009 runner-up finish to Rafael Nadal.
Last year Murray was bundled out in the third round, but he was hoping for much better as he arrived fresh off his 45th career ATP title in Dubai.
Murray was particularly disappointed to have dropped the first set after twice going up a break.
But he hurt his own cause with seven double-faults, part of a poor serving night that he said was key to the defeat.
Pospisil had never beaten Murray in four prior encounters. The 26-year-old, who defeated Taiwan's Lu Yen-Hsun in the first round as Murray enjoyed a bye, notched his fourth career victory over a top-10 player and his first since 2014.
Late last year he began working with Australia's Mark Woodforde -- and he gave a shout-out to his new coach on court after wrapping up the biggest win of his career in one hour and 51 minutes.
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