Another notable casualty on the first day of competition was former world No. 1 Ana Ivanovic, who surged ahead in the first set against world No. 12 Carla Suarez Navarro but lost 2-6 6-1 6-2 after two error-strewn sets.
With U.S. Secretary of State John Kerry and gymnastics gold medal favourite Simone Biles looking on, seven-times grand slam winner Williams won the first set but became frustrated as the match wore on, losing 4-6 6-3 7-6(5) to the world number 62.
Flipkens collapsed on to the court after winning the final set tie-breaker and the rowdy Brazilian crowd serenaded her with chants of "ole, ole, ole".
Flipkens later thanked the "amazing" Brazilian crowd for helping her pull off one of the biggest wins of her career.
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"To beat Venus Williams on the centre court, one of the biggest champions in our history, that (gave me) goosebumps all over the place," she told reporters.
The loss will not be the end of the competition for 2000 Sydney Games champion Williams, however, as the 36-year-old is bidding to win her fourth doubles gold medal with sister Serena.
Former French Open winner Ivanovic rued letting her chances slip away.
"I had a chance to come back in the third set but every time I came close to pegging her back, I missed the opportunity," said the world No. 26.
Ivanovic's match, like all the others on centre court, was played in a stadium that was more than half empty, something likely to disappoint organisers.
But the size of crowds did not bother Japan's Kei Nishikori, who opened the men's singles tennis tournament on centre court by knocking out Spain's Albert Ramos-Viñolas with ease, winning 6-2 6-4 in two sets.
Some players said conditions were tricky due to soaring temperatures and a strong breeze drifting across from the ocean.
"Here it’s very difficult to play because it’s fairly open, there is constantly some kind of wind," said Croatia's Marin Cilic, who beat Bulgaria's Grigor Dimitrov 6-1 6-4.
One player who thrived in the Rio sun was Australia's John Millman, who become the first Olympian to win a men's singles match without losing a game.
Millman's "double-bagel" 6-0, 6-0 victory came against Lithuania's Ricardas Berankis. The Australian, who has battled back to fitness after several shoulder surgeries that threatened his career, took part in Friday's late-night opening ceremony, which many Olympians competing early on Saturday skipped.
"That was a really stirring moment for me. It's hard to explain the emotions I got walking into that stadium, and obviously that carried over to today," said the 27-year-old.
(Reporting by Drazen Jorgic and Liana Baker in Rio De Janeiro; additional reporting by Josh Schneyer; Editing by Tom Brown/Peter Rutherford)
