Romania's Halep, who is also a former Grand Slam winner on this surface, beat Alizé Cornet from France 6-4, 6-4 on the Foro Italico clay in Rome.

Cornet's serve was broken six times across a back-and-forth affair in which she actually had a better record on her second service than first.

Halep reached the final of this Women's Tennis Association (WTA) 1000 tournament in 2017 and 2018 before finally triumphing in 2020.

American seventh seed Danielle Collins will face Halep in round two.

Bencic defeated home player Elisabetta Cocciaretto 6-4, 6-2.

Eighteen-year-old American Coco Gauff was too strong for Germany's three-time Grand Slam winner Angelique Kerber and won 6-1, 6-4 to reach round two.

Canada's Leylah Fernandez, 19 and the US Open runner-up last year, came from behind to knock out 14th seed Anastasia Pavlyuchenkova 1-6, 6-2, 6-2.

Pavlyuchenkova is Russian but allowed to play as a neutral under WTA rules.

Another such athlete, Daria Kasatkina, awaits Fernandez in round two after seeing off Slovenia's Tamara Zidanšek 6-4, 6-3.

The top eight seeds, including world number one and defending champion Iga Świątek of Poland, get a bye into round two.

The men's event also began today and like the women's only saw one seed knocked out.

American giant Reilly Opelka was that man, falling 3-6, 7-5, 2-6 versus Wawrinka.

Wawrinka is a three-time Grand Slam champion but had not won a match since February 2021, at the Australian Open.

Austria's Dominic Thiem, like Wawrinka on the comeback trail after a torrid time with injury, had no such joy and lost to Italy's Fabio Fognini in straight sets.