Top-ranked Novak Djokovic cruised into the second round of the US Open on Monday while Japanese fourth seed Kei Nishikori crashed out after his runner-up effort last year. And three-time defending women’s champion Serena Williams, the world number one trying to complete a calendar grand slam, saw three top rivals fall as she eased into the second round. Rafa Nadal, meanwhile, showed flashes of his top form to beat young Croat Borna Coric 6-3, 6-2, 4-6, 6-4 in the last match of the night. I’m just hoping I can continue to play this way and if I can, I feel I have a really good chance against anybody Novak Djokovic Djokovic needed only one hour and 11 minutes to capture a 6-1, 6-1, 6-1 victory over Brazil’s Joao Souza. “There’s something I love about number one for sure. Hopefully I can keep it up,” said Djokovic. “I’m just hoping I can continue to play this way and if I can, I feel I have a really good chance against anybody.” Djokovic’s highest-ranked possible semi-final foe had been Nishikori, but last year’s US Open runner-up exited the US Open at the first match for the third time in five years as France’s 41st-ranked Benoit Paire saved two match points and defeated the Japanese star 6-4, 3-6, 4-6, 7-6 (8-6), 6-4. “To beat Nishikori, for me, it was impossible to imagine this,” Paire said. “I’m really happy.” Top-10 women’s seeds Ana Ivanovic, Karolina Pliskova and Carla Suarez Navarro exited with opening-match losses, leaving 12th seed Belinda Bencic as the top-rated foe in Williams’ half of the draw. Williams, who lost to Bencic in the Toronto semi-finals, could face the Swiss teen again in the quarter-finals as she chases the first calendar grand slam since Steffi Graf in 1988 and a 22nd career major title to match Graf’s open era record. Williams was leading 86th-ranked Russian Vitalia Diatchenko 6-2, 2-0 when Diatchenko retired after just 30 minutes at Arthur Ashe Stadium with a left foot injury. Williams, 33, advanced to a second-round match against Dutch qualifier Kiki Bertens, who eliminated Croatian Mirjana Lucic-Baroni 3-6, 6-4, 6-2, and would face an American in the third round, either 19th seed Madison Keys or Coco Vandeweghe. Paire, who had never before beaten a top-five foe, fired 21 aces to only three for Nishikori and blasted 64 winners, 30 more than Nishikori, with 67 unforced errors, 31 more than the Asian number one. “He was very aggressive, so there were many rallies and it was tough to get rhythm,” Nishikori said. Nishikori enjoyed his highest seeding for any grand slam event all-too briefly, walking off Louis Armstrong Stadium with his head down. Nishikori led the tie-breaker 6-4 but swatted a forehand long, watched Paire smack two service winners and then Nishikori netted a forehand to force a fifth set. Paire, who won his first ATP title last month at Bastad, broke for a 3-2 lead and held to the finish to win after three hours and 14 minutes. “To be honest, I think I’m lucky,” Paire said. “Today, for me, it’s a good day. I’m really happy to win.” Nishikori had won three titles this year, including a US Open warm-up win at Washington that saw him avenge last year’s US Open final loss to Croatian Marin Cilic. “It’s very sad always to lose first round,” Nishikori said. “I think it was more because of him I wasn’t playing 100 per cent.” Cilic won his opener 6-3, 7-6 (7-3), 7-6 (7-3) over Argentine qualifier Guido Pella. “Defending a grand slam title for the first time for sure is something I will learn from,” Cilic said. On the women’s side, Slovakia’s 50th-ranked Dominika Cibulkova ousted seventh-seeded Ivanovic 6-3, 3-6, 6-3, delivering the Serb star’s earliest US Open exit since 2009. “It’s definitely very disappointing with the loss because I felt like I had great preparation,” Ivanovic said. “I felt like I’ve been improving. That’s why it’s so disappointing. I just have to keep working.” After the injury-forced withdrawal of Russian third seed Maria Sharapova, Ivanovic had been Williams’ top-ranked rival. That status fell to Czech eighth seed Pliskova, who promptly lost to American Anna Tatishvili 6-2, 6-1, and then to 10th seed Suarez Navarro, who fell to Czech Denisa Allertova 6-1, 7-6 (7-5). One Williams rival who advanced was her older sister Venus, a seven-time grand slam champion. The US 23rd seed outlasted Puerto Rico’s Monica Puig 6-4, 6-7 (7-9), 6-3.