Maria Sakkari sealed victory for top-seeded Greece over Bulgaria in the United Cup with a straight sets win over Viktoriya Tomova.
Team-mates Stefanos Tsitsipas and Despina Papamichail had already won their matches on Thursday, and Sakkari's 6-3 6-2 triumph gave Greece an unassailable 3-0 lead.
Michail Pervolarakis was defeated by Dimitar Kuzmanov in the final singles match between the nations, but Tsitsipas and Sakkari teamed up to earn Greece a 6-4 6-4 success in the doubles encounter to end on a high.
World number 16 Matteo Berrettini helped Italy topple Brazil by overcoming Thiago Monteiro 6-4 7-6 (9-7).
That gave Italy a 2-1 lead, and Lucia Bronzetti finished the job by demolishing Laura Pigossi in straight sets, with Brazil powerless to overturn the deficit despite Berrettini and Camilla Rosatello's defeat in the doubles match.
US Open semi-finalist Frances Tiafoe clinched a win for the United States over the Czech Republic after opponent Tomas Machac retired with an ankle injury with the score at 6-3 2-4.
Petra Kvitova had defeated Jessica Pegula 7-6 (8-6) 6-4 in the third singles match to give Czech Republic hope, but Tiafoe's win settled the contest before Pegula and Taylor Fritz joined up for success in the doubles.
Great Britain were 3-2 victors over Australia despite a pair of defeats on day two in Sydney.
Cameron Norrie's triumph over Nick Kyrgios' replacement Alex De Minaur on day one had helped Great Britain to a 2-0 lead over the hosts, and Harriet Dart prevailed over Maddison Inglis to wrap up the victory.
Dan Evans was then beaten 6-3 7-6 (7-3) by Jason Kubler before Dart and Jonny O'Mara fell to defeat in the doubles, but Great Britain's strong start saw them through.
France and Switzerland completed 5-0 sweeps of Argentina and Kazakhstan respectively, with Caroline Garcia winning both her singles and doubles matches in straight sets while Stan Wawrinka saw off Alexander Bublik 6-3 7-6 (7-3).
World number one Swiatek sees off Xiyu in Madrid opener
World number one Iga Swiatek overcame Wang Xiyu with the minimum of fuss on Thursday to progress to the third round of the Madrid Open.
Swiatek has yet to win the title in Madrid, which is the only clay-court European event at which the Pole has not triumphed, but she got off to a flying start with a 6-1 6-4 victory over Xiyu.
"I love this place. I got to know the city a little better last year," Swiatek said. "So this time I feel more comfortable around."
Next up for the 22-year-old is a third-round tie against 27th seed Sorana Cirstea on Saturday.
Data Debrief
Swiatek has registered 150 match wins on the WTA Tour since the start of 2022. Elena Rybakina and Coco Gauff are the next best with 108 wins each.
She also became the first player born this century to claim 50 combined match wins in Madrid, Rome and Roland-Garros, since the inaugural women's singles event at the Madrid Open in 2009.
Dominant Gauff double bagels Rus at Madrid Open
Coco Gauff made a flying start to her Madrid Open campaign on Thursday, recording the first double bagel main-draw win of her career as she cruised past Arantxa Rus to reach the round of 32.
Gauff needed just 51 minutes to see off 33-year-old Rus as she booked a meeting with Ukraine's Dayana Yamstremska for Saturday.
The US Open champion lost just 18 points throughout the match – eight in the opener and 10 in the second set – as she put any doubts over her recent form to bed in emphatic fashion.
Gauff's power proved too much for Rus in the opener, the third seed winning 88 per cent of points behind her first serve and converting three of four break points to go a set up in just 23 minutes.
Rus brought up four break points midway through the second set, but when she failed to convert them, Gauff punished her in ruthless fashion by reeling off another three games then finishing things with a terrific forehand winner.
Speaking after her win, the American said: "I played really well today. It was just one of those days for me… 6-0 6-0, I've never done that before, I'll probably never do it again."
Data Debrief: Gauff matches Azarenka, Halep feat
Gauff is just the third player to register a 6-0 6-0 win in the women's singles draw at the Madrid Open, following in the footsteps of two former world number ones in Victoria Azarenka and Simona Halep.
The American, who only turned 20 last month, is also the youngest player to double bagel an opponent in any main-draw match on the WTA Tour since Iga Swiatek did so against Karolina Pliskova in the 2021 Italian Open final in Rome.
Nadal cruises past teen Blanch to tee up De Minaur rematch in Madrid
Darwin Blanch presented little challenge for Rafael Nadal, who dropped just one game in a convincing 6-1 6-0 triumph at the Madrid Open.
Nadal is feeling his way back to fitness, but 16-year-old qualifier Blanch offered little resistance to the 22-time major champion on Thursday.
Making his farewell appearance at the Madrid Open, where he has won five titles, Nadal needed just 64 minutes to progress to round two.
"I think today I played against an opponent with a great future in front [of him], but today, still making mistakes," said Nadal.
"I just tried to be there, be solid all the time without taking a lot of risks. It worked well. I'm happy to be through and I wish him all the very best for the future."
Nadal's reward is a rematch with Alex de Minaur, who he lost to last week in Barcelona.
Data Debrief
This game saw the largest age gap (21 years, 117 days) between two opponents in the history of ATP Masters 1000 events.
Nadal has now registered 57 wins at the Madrid Open, which is 20 clear of any other player.
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