Coco Gauff and Taylor Fritz were in fine form at the United Cup on Tuesday, clinching the United States a place in the quarter-finals by beating Croatia.

Fritz got the USA to the perfect start, cruising past Borna Coric in straight sets to prevail 6-3 6-2 in just over an hour and a half in Perth, registering his first-ever ATP win over the Croatian despite a shaky start.

Gauff then followed it up with an equally impressive win, getting the better of Donna Vekic 6-4 6-2 later on Tuesday.

The last meeting between the pair while representing their countries came at the Paris Olympics, with Vekic claiming a shock victory on her way to a silver medal, but Gauff was in control this time around.

"I'm really happy with how I played," Gauff said post-match.

"She's a great player, and the Olympics loss hurt, so I definitely was thinking about it as motivation to do better."

Gauff and Fritz then teamed up in the doubles to finish the round with a perfect 3-0 score, beating Ivan Dodig and Petra Marcinko 6-2 6-3.

The reigning champions, who saved all three break points they faced in the doubles match, qualified as Group A winners.

Meanwhile, Italy also booked their place in the quarter-final, with Flavio Cobolli fighting back from the verge of defeat to beat Ugo Humbert 3-6 7-6 (10-8) 6-2 and help them top Group D.

Humbert looked set to give France the advantage, having won the first set 6-3, he was serving for the match at 5-4 in the second before Cobolli flipped the script.

The Italian broke his serve to level the score before winning the tie-break and easing to victory.

"I think that we did a great match. It was a great battle to start the season, so I'm really happy about the match," Cobolli said.

"I think I played a really good match, and also it was tough to come back [against] Ugo. Congrats also for him and I wish him good luck for his season."

Jasmine Paolini then followed that up with a comfortable 6-0 6-2 victory over Chloe Paquet, who had beaten this year's French Open and Wimbledon finalist in their only previous meeting in 2019.

"I'm happy with my performance. I was focused every time. I think [everything worked] pretty well," Paolini said.

"I'm happy, as well, that Flavio won an amazing match. Unbelievable. He was a set and break down. He turned the match. Unbelievable."

Sara Errani and Andrea Vavassori then ensured a clean sweep for Italy, holding on to claim a 6-3 7-6 (7-3) win in the doubles over Edouard Roger-Vasselin and Elixane Lechemia.