In conditions that were hot but not extreme, the Scot struggled badly with cramp during the last two sets but survived to win 6-3 7-6 (8/6) 1-6 7-5.
Haase, who was also troubled physically, served for the fourth set but could not take advantage of Murray’s discomfort.
Murray came out for the fourth set with the clear intention of trying to make points short but he looked close to cramping and Haase made it nine games in a row to move into a 3-0 lead.
Ice was eventually brought, which Murray placed on his left thigh, and he finally stopped the rot to make it 3-1.
He still looked very uncomfortable but it was Haase who called for the trainer after the fifth game for treatment to his foot.
Murray was having some success on his opponent’s serve despite his troubles and three times brought up break point in the seventh game.
The return winner he hit to create the last of those opportunities seemed to bring on cramp all down Murray’s right side but he took the next point with an aggressive return.
Murray did not sit down at the changeover in an attempt to keep the cramp at bay but he dropped serve once again to leave Haase serving to make it two sets all.
The Dutchman made a mess of it, though, handing Murray the break back with a double fault, and two games later the 2012 champion brought up the chance to serve for the match with a forehand thumped onto the sideline.
Still it was not straightforward, Murray having to save three break points before finally clinching victory after a gruelling three hours and eight minutes.