Pospisil’s win was even more creditable as he staged a comeback from being a break down in the first set. Trailing 4-2 in the first set, the 26-year-old won six straight games as he went up a break in the second set before Murray broke back to level the score at 2-2.
The second set went into a tiebreaker in which Murray saved three match points before Pospisil converted the fourth to seal a famous win.
“I felt like I had the ability to do it, but going through it is another thing,” Pospisil said.
“I was just kind of sticking to the game plan and kind of distracting my mind with what I wanted to do on the court.”
“Of course still some thoughts come in, especially in the second set. It's not every day you're close to beating the number one player in the world. So I did well to kind of stick with the process and not really get distracted,” he said.
In the other upset of the tournament, Italy’s Fabio Fognini shocked French seventh seed Jo-Wilfried Tsonga 7-6 (7/4), 3-6, 6-4 to reach the third round.
Fognini, ranked 43rd in the world, registered his first win over eighth-ranked Tsonga in five meetings.
In other matches, eighth-seeded Austrian Dominic Thiem beat Frenchman Jeremy Chardy 6-2, 6-4 while Japan’s Yoshihito Nishioka upset 19th-seeded Ivo Karlovic 6-4, 6-3. Former finalist John Isner moved into the third round with a 7-6 (7/0), 7-6 (8/6) victory over Kazakhstan's Mikhail Kukushkin.