Pospisil, ranked 129th in the world, was rewarded for his aggressive approach, rushing the net whenever the opportunity arose and pouncing on Murray's second serve.
"I knew I was a long shot. I've played Andy four times and didn't win a set," the 26-year-old told Tennis Channel.
"I felt like I had the ability to (win) but to actually go through is a whole new thing. I tried to bring different tactics ... versus the other times I played him.
"I didn't want to give him the same look each time. I wanted to put pressure coming into the net, using my strength, which is my ability at the net and serving well."
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Pospisil joked that his lowly current world ranking was due to a "mid-life crisis" that saw him endure a lean 2016, after he had made the Wimbledon quarter-finals in 2015.
Earlier, Italian Fabi Fognini won a battle of expectant fathers when he beat Jo-Wilfried Tsonga 7-6(4) 3-6 6-4.
Unseeded Fognini survived a first-set tiebreak and a tense final set before upsetting the seventh-seeded Frenchman in a match that stretched nearly two hours and 30 minutes in the blazing afternoon sun.
"I am happy about my performance. It's a good victory for sure," Fognini told Tennis Channel after beating Tsonga for the first time in five career meetings.
"Today was really hot so the ball was bouncing a lot. I love playing with sun and good weather."
Fognini considered himself fortunate even to make it to the second round.
The Italian dropped the first set to love and was down 5-2 in the second set of his first-round encounter with Russian Konstantin Kravchuk, before roaring back to win 0-6 7-5 6-4.
"It is a crazy sport," Fognini said.
Fognini's wife, 2015 U.S. Open champion Flavia Pennetta, is expecting a child in late May, while Tsonga is also set to become a father next month.
In another upset on Saturday, Japanese world number 70 Yoshihito Nishioka beat Croatian veteran Ivo Karlovic 6-4 6-3, but seeds Dominic Thiem, David Goffin and Tomas Berdych won their matches to advance.
(Reporting by Andrew Both in Cary, North Carolina, editing by Gene Cherry/Peter Rutherford)
