Veteran Williams managed to win the opening set tie-breaker 8-6 and hit 32 winners in the match, sending a brief reminder of her old form.
A seven-time Grand Slam champion, Williams has long fallen into the background behind younger sister Serena, who will be shooting for the Calendar Year Grand Slam and attempt to win her 22nd major title at the US Open in a couple of weeks.
"Preparations are underway (for the US Open) but it still doesn't feel that close," Venus told reporters. "My opponent (Diyas) played so well today. She was so determined out there."
Venus will now face ninth-ranked Ivanovic, seeded sixth in the tournament, in the second round.
The tournament's opening day featured a couple of upsets as ninth seed Garbine Muguruza of Spain went down to Yaroslava Shvedova 6-4 7-6. Timea Bacsinszky, the 12th seed, also fell to Madison Keys 6-4 6-3.
Germany's Andrea Petkovic and former world number one Jelena Jankovic both advanced.
(Writing by Jahmal Corner in Los Angeles; editing by Sudipto Ganguly)
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