Boulter set up her second-round meeting with Zheng by beating another Chinese player in world number 61 Yue Yuan in the first round.
Boulter, ranked 54th, also beat world number three Jessica Pegula at the United Cup team event at the start of the season and came through qualifying to make the Adelaide International main draw.
Zheng controlled their first set on Thursday and after Boulter broke serve for a 3-2 lead in the second, the Briton double-faulted twice in blustery conditions in the next game as she gave up the advantage.
The match was then decided in a marathon ninth game with Zheng clinching her sixth match point, having saved six Boulter break points.
Boulter remained positive despite the defeat.
“This trip has been great,” the 27-year-old said. “For me, it’s about week in, week out playing these girls, trying to get big wins against the best players in the world.
“It is a massive step in the right direction.
“I don’t think my tennis is far behind. I think I had a lot of chances, as well.
“She’s an incredible player with a lot of wins under her belt, as well. So I have to factor that in. Ultimately I feel like I can challenge these girls on a daily basis.”
Following her singles defeat, Boulter played in the women’s doubles alongside Petra Martic, but the two lost their first-round match against fifth seeds Laura Siegemund and Barbora Krejcikova 6-2 6-1.
In the men’s doubles, Britain’s Henry Patten, playing with Portugal’s Francisco Cabral, beat Australian pair Tristan Schoolkate and Adam Walton 6-3 6-7 (6-8) 7-6 (10-4).
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