The Brit has never won in Indian Wells and will have to wait another year for a shot at the title after this surprise second-round defeat to the world No 129.
Murray, the world’s top-ranked player, had won all four of his previous meetings with Pospisil but was sluggish throughout and went down in an hour and 52 minutes.
The 29-year-old was broken four times in total by Pospisil, who celebrated his biggest-ever win on the ATP Tour to secure a third-round clash against Dusan Lajovic.
Jo-Wilfried Tsonga was also dumped out by Fabio Fognini with the Italian winning 7-6 (7/4) 3-6 6-4 in a clash which lasted just shy of two-and-a-half hours.
After winning the first set on a tie-break, Fognini lost the second to seventh-seeded Tsonga but recovered well to win a nervy third.
Stan Wawrinka, seeded third, had an easier time of it by beating Paolo Lorenzi 6-3 6-4 and Gael Monfils also progressed with a 3-6 6-0 6-1 triumph over Barbados’ Darian King.
Serbian qualifier Lajovic was a surprise 6-2 4-6 7-6 (7/2) winner against 30th seed Feliciano Lopez of Spain and Ivo Karlovic also suffered a second-round exit to Japan’s Yoshihito Nishioka, who triumphed 6-4 6-3.
Pablo Carreno Busta beat Peter Gojowczyk 7-5 6-2 while David Goffin, seeded 11th, was made to work for his 6-4 3-6 6-3 victory over Karen Khachanov.
Tomas Berdych is also safely through to round three after a 7-6 (7/4) 6-4 win against Bjorn Fratangelo while John Isner won two tie-breakers to triumph 7-6 (7/0) 7-6 (8/6) over Mikhail Kukushkin.
There were also second-round wins for Mischa Zverev, Dominic Thiem, Roberto Bautista Agut, Albert Ramos-Vinolas and Pablo Cuevas while Philipp Kohlschreiber benefited from Alexandr Dolgopolov’s retirement.