Williams, 35, made over 70 unforced errors in the scratchy display where she won the title last year to kick off a standout season that saw her claim the WTA's Comeback of the Year award after two other tournament wins in China.
Former French Open champion Ivanovic had little answer to the supreme serving of British qualifier Naomi Broady, who racked up 14 aces in a 7-5 6-4 win.
The 25-year-old from Manchester maintained her first serve percentage at almost 70 as she took out the second seeded Serb to leave the $250,000 tournament shorn of its headline acts.
Dane Caroline Wozniacki was not at her best on the blue New Zealand hard courts but avoided making it a hat-trick of first round exits by former world number ones as she beat Danka Kovinic of Montenegro 6-4 6-4.
(Writing by Patrick Johnston in Singapore; Editing by John O'Brien)
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