Recovering from 2-0 down in the second set, Williams was on the brink of victory with a 5-3 lead when rain forced the players off court.
Venus Williams was able to focus on Wimbledon despite her involvement in a recent fatal car crash as the five-time champion beat Elise Mertens 7-6 (9/7), 6-4 in the first round on Monday.
Williams is being sued by the estate of an elderly Florida man who died last month after his vehicle was hit by a car driven by the American star.
The 37-year-old is accused of running a red light, inattentive driving and negligent operation of a vehicle, leaving Jerome Barson with a fractured spine and numerous internal injuries before his death several weeks later.
Williams, who owns a home near the crash site, last week said she was "heartbroken" over the tragic incident as she prepared to make her 20th appearance at Wimbledon.
The world number 11 put the horror crash to one side as she advanced to the second round, where she will face China's Wang Qiang.
Making her first appearance in the Wimbledon main draw, Mertens, 21, was just one when Venus made her Wimbledon debut in 1997.
Mertens, ranked 54th, was playing only her fifth career Grand Slam match, while Williams is a seven-time Grand Slam winner and reached the Wimbledon semi-finals last year.
Despite that vast gulf in experience, Mertens wasn't overwhelmed when Williams, the oldest player in this year's women's singles event, won the first three games on Court One.
The Belgian hit back to force a tie-break and saved four set points before Williams finally edged in front.
Recovering from 2-0 down in the second set, Williams was on the brink of victory with a 5-3 lead when rain forced the players off court.
Mertens had saved two match points before the weather intervened, but Williams sealed the win after the resumption on her fifth match point.
Recovering from 2-0 down in the second set, Williams was on the brink of victory with a 5-3 lead when rain forced the players off court. Read Full Story
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