The score was a surprise given Zhang's impressive run in Doha last week when she beat Garbiñe Muguruza en route to the quarterfinals.
But she found her Croatian opponent on devastating form, producing a display of awesome power hitting to seal a second-round meeting with Australia's Sam Stosur.
"The last two years I played quallies, so I'm really happy to be in the main draw this year and to keep my game like that," said Konjuh. "Hopefully I'm going to continue."
A Chinese player who fared much better was Peng Shuai, who comfortably defeated Leisa Tsurenko 6-1, 6-1 to set up a second-round clash with Barbora Strycova. Surprises continued on Court 1 with Catherine Bellis eliminating 17th seed Yulia Putintseva 6-1, 7-5. Meanwhile, qualifier Elise Mertens upset Tsvetana Pironkova 6-3, 6-2 on Court 3.
Bellis, ranked 70th in the world, found herself 5-1 down in the second set before reeling off an incredible six games on the trot to seal a remarkable victory.
"I got myself in a bit of trouble in the second set, but I'm glad I got out of it. I just thought to myself, stick to my game plan, just keep steady, I can come back," said Bellis afterwards. "I can come back against anyone I set my mind to. I'm really glad I got through it. in the beginning of the second, I think I won the first game. The second game was really long.
"So I just kept thinking to myself, I'm still in this match, obviously even when I was losing, still in this match, and I'm playing well, so I can come back whenever I want and whenever, you know, I get a good rhythm. So once I went down, I just stayed calm and stuck to my game plan and came back."
Elsewhere, Kateryna Bondarenko survived an opening-set blip to come through 4-6, 6-4, 6-3 against Aryna Sabalenka of Belarus. Misaki Doi claimed a notable win against Madison Brengle, the Japanese beating the American in three tight sets.
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This article was first seen on www.wtatennis.com.