The British No 1 took full advantage of an error-strewn display from the Dutchman as he completed a 6-1 6-1 6-4 win in just 88 minutes on Court One.
Murray will next face Italian 25th seed Andreas Seppi or Croatia’s talented 18-year-old Borna Coric??in round three.
After battling through against Mikhail Kukushkin in his opening match of the tournament, Murray enjoyed a much more straightforward win against an out-of-sorts Haase.
The third seed dropped only one point on serve in the first set as he broke his 78th-ranked opponent three times to take it 6-1 in just 20 minutes.
Murray’s momentum continued at the start of the second set as he earned a??fourth successive break to move 3-0 ahead.
A slight lapse in concentration from the 2013 champion in the fourth game gave Haase his first break-point chance, but he was unable to take advantage as the Brit recovered to hold serve.
That would be the Dutchman’s only break point of the match and the second set soon slipped away from him as Murray broke again to take it 6-1.
Haase threw caution to the wind at??the start of the third set, unleashing a thundering forehand winner, which was??greeted with raptures of encouragement from his box.
Even a few British voices were urging Haase on and the more aggressive approach??paid dividends during a short spell of parity.
For every winner from Haase, however, there was also an unforced error and??Murray capitalised in the seventh game to claim another break.
Haase continued to blast away until the end but Murray was more than able to??keep up as a thumping backhand of his own sealed a comfortable victory.