The third-seeded Scot had few problems with the 53rd-ranked Haase and was always in charge of his opening match, breaking Haase's service eight times in a dominant display, reports Xinhua.
"It was a good start and it was nice to win in straight sets," said Murray, who broke through for his first Grand Slam title at last year's US Open.
"Today is the hottest day of the tournament," Murray said. "It took a little while to get used to that and the court was playing much quicker because of it."
Murray, twice runner-up at the Australian Open, is drawn to face 17-time Grand Slam winner Roger Federer in the semifinals and possibly defending champion Novak Djokovic in the final.
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