It was his first win against the world number 56 in three attempts and came without a single break point conceded. "He mixes it up well with his slice and serve, so he's always a hard opponent on this surface", said Zverev, the world number 12.
A break of serve in each set was enough for the Italian Open champion to reach his seventh quarter-final of the season, where he will take on seventh-seeded Spaniard Roberto Bautista Agut.
Haase saved three set points en route to a 6-3 7-6 (9/7) victory, which secures his first quarter-final in Halle at the fifth attempt.
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But Sunday's turnout hit a record low of 49 percent, mirroring the French people's growing disinterest in legislative elections. The election took place amid heightened security after a series of devastating terror attacks in recent years.
"I'm very satisfied because Philipp is someone who can play very well on grass", Zverev told the official ATP website.
"It was not the best start I've had".
"I hope to get some matches next week (in Antalya) and then get ready for Wimbledon".
The second set followed a similar pattern, as Tomic struggled to overcome the Frenchman's excellent returning game and was broken two further times to sink to defeat in exactly one hour.
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