Konjuh, a 16-year-old ranked No. 259, took out the 14th-ranked Vinci 3-6, 4-6, 6-2. Konjuh lost just six points in her four games serving in the final set.
Vinci finished off five of her six break chances but didn't have any such opportunities in the final set. Konjuh won half the points off Vinci's serve, including going 7-of-14 in break chances.
Konjuh's win was one of four over seeded players Tuesday in Auckland. Qualifier Sharon Fichman dumped No. 4-seed Sorana Cirstea 6-1, 6-4 by taking nearly 60 percent of the points in the match. Ayumi Morita was a 7-6 (7-2), 6-3 winner over sixth-seeded Lucie Safarova and Julia Goerges ousted No. 8-seed Karin Knapp 4-6, 7-6 (7-3), 7-6 (7-2) in a 2-hour, 40-minute match.
Second-seeded Ana Ivanovic battled for nearly 2 hours before coming away with a 7-5, 7-6 (7-2) winner over Alison Riske and No. 3-seeded Kirsten beat Monica Puig 6-4, 7-5 with six breaks.
Also in the first round, Lauren Davis defeated Marina Erakovic 6-1, 6-4; Kristyna Pliskova ran past Yanina Wickmayer 7-6 (7-3), 6-0; and Sachie Ishizu topped Anett Kontaveit 6-3, 1-6, 6-3.