The second-seeded Murray, who had a bye in the first round, dropped serve while leading 3-2 in the second set but held off five more break chances for Pospisil. The Canadian had 27 aces in his first-round win over Daniel Brands of Germany but just three against Murray.
"It was a tricky match to start with. He serves well and is a quick mover," Murray said. "It was hard. It was the first time I played indoors since Rotterdam, which was seven, eight months ago. And it's always different to play indoors ... the match could've definitely been a lot closer."
Murray decided only last Friday to accept a wild card as he is chasing points in order to qualify for the ATP Finals in London next month.
"Hopefully, I can improve for my next game," the Scot said after his 470th career win. He joined Fabrice Santoro in 50th place on the Open era win list.
Pospisil, from Vancouver, had eight double-faults and lost serve late in each set as the 11th-ranked Murray imposed his game in their first career meeting.
"I felt like overall I played well from the baseline, but my serve let me down for sure," said Pospisil. "I can't remember when I had so many double-faults and such a low first-serve percentage.
"Other than that it was a good match. I had chances in both sets but Andy played well when he had to."
Pospisil, the world No. 44, fell to 19-21 on the season.
He will return to action next week at the Swiss Indoors. Pospisil reached the semifinals last year in Basel before falling to Swiss star Roger Federer.
""My goal is to try and finish the season strong," Pospisil said. "Both Basel and Paris are big events with a lot of opportunities. I want to get in some good matches and hopefully play well."
Murray next plays Jan-Lennard Struff of Germany, who won the last seven points in the third-set tiebreaker to beat Sergiy Stakhovsky of Ukraine 7-6 (6), 2-6, 7-6 (3).
David Ferrer advanced to his 15th quarterfinal of the season after defeating Tobias Kamke of Germany 7-5, 6-1. The fifth-ranked Ferrer, the top seed, avoided service breaks and converted his second match point with a forehand winner.
"It was tough in the first set but in the second I played better, more solid, more consistent," said Ferrer, who plays No. 6 Ivo Karlovic of Croatia in the quarterfinals.
The Spaniard needs to reach Sunday's final to improve his chances of qualifying for the ATP Finals.
Earlier, Thomaz Bellucci of Brazil rallied to beat the 2004 champion, No. 3 Feliciano Lopez, 6-7 (9), 6-1, 6-4.
Lopez, who was ranked a career-high 14th after beating Rafael Nadal on his way to the Shanghai semifinals last week, lost eight straight games from 1-1 in the second. The Spaniard also lost 19 points in a row, including the first 13 of the final set.
Bellucci will meet Viktor Troicki of Serbia, who reached his third quarterfinal since returning from a doping ban in July by beating No. 5 Lukas Rosol of the Czech Republic 6-3, 6-2.
Also, Benjamin Becker of Germany defeated last year's finalist, Robin Haase of the Netherlands, 6-3, 6-3, winning six straight games to lead by a set and 2-0. He lined up a quarterfinal against compatriot Philipp Kohlschreiber.
With files from The Canadian Press.