Hitting 34 winners, the Brit came from behind after a sluggish start that saw him drop the first set in just 34 minutes. After rallying to claim the second set in a tiebreaker, Murray again fought back, this time from a 3-0 deficit in the third set to claim victory.
Murray finishes with a flourish in three-set thriller
Haase got off to a good start, saving two break points in his first service game and firing a backhand winner up the line to bring up two break points. Saving the first, Murray misfired on a backhand to give the Dutchman a 2-1 lead.
The 198th-ranked wild card was soon up a double break at 4-1 after the 2008 Rotterdam champion again was wayward with a backhand and after Haase fired off a big serve, he was off to a one-set advantage.
After six straight comfortable holds, Murray saved a pair of break points in the seventh game to keep his nose in front. He ran away the tiebreaker behind two minibreaks to level the match.
Murray was broken in the second game of the deciding set and after a hold, Haase raced out to a 3-0 lead only to see the former world number one roar back, claiming six consecutive games to seal a spot in the second round.