Thursday's match was just Venus Williams's seventh of the year and first since January's Australian Open, where she fell to Simona Halep in the round of 32.
The Danish World No 3 ended 2017 with the biggest title of her career in Singapore and returned a day after thrashing Madison Brengle in her season opener to hit 21 winners against eight unforced errors in the 53-minute win over Martic.
Karolina Pliskova lost her cool over a line call and bashed a hole into the umpire's chair with her racket after suffering a 3-6, 6-3, 7-5 defeat by Maria Sakkari in the Italian Open second round on Wednesday.
A summary of sports events and persons who made news on Friday
Images from Day 5 of the US Open in New York on Friday
Former world number one Andy Murray withdrew from the Brisbane International with a hip problem on Tuesday, further putting in doubt the Briton's prospects of being fit in time for the Australian Open later this month.
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