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.
"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 had 27 aces in his first-round win over Daniel Brands of Germany but just three against Murray.
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).
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"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.
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.