The Scot was far from his fluent best, blighted by hurting his ankle and ongoing frustrations with his own performance, but did enough to win 6-3 7-5.
A back-and-forth second set saw both players trade relentlessly from their base-lines. Pospisil led 5-3 but was overpowered as Murray recovered to close out the match and advance to the last eight.
The Canadian threatened to break early in the match after holding his own during rallies and although he couldn???t, Murray went into the break querying the time spent between games with the umpire.
Pospisil gave up a break point without working Murray too hard to make it 5-3 in the opener and the British No 1 sprinted to the end of the set in a total of 36 minutes. He had only registered five winners in the whole set.
Moments into the next set Murray limped out of a dash across his base-line, his grimacing face indicating a painfully turned ankle, and he only just held his service game.
Cursing and berating his own game, Murray pushed forwards to the net to win a break point and go 3-2 ahead in the second set but wouldn???t see things out as smoothly as he hoped.
A brilliant return down the line from Pospisil earned him an immediate break and he held his serve to go 4-3 ahead, screaming his delight in Murray fashion.
The 24-year-old began to find success; a wonderful lob followed by a volley won a point after Murray angrily wrecked his racket.
With Pospisil 5-3 ahead in the second set the tide dramatically changed, one long and gruelling point with 30 shots was edged by Murray who went on to win break point.
Pospisil did little against Murray???s serves and continually struggled to match the Scot???s legs and strength when they rallied from the base-line.
Murray soon found himself at five apiece in the second set and an intense, edgy break of serve put him 6-5 up and allowed him to serve out the match and advance into the next round.
Murray will meet the Frenchman Gilles Simon in the quarter-final.