Jessica Pegula began her US Open campaign with a convincing victory on Sunday, recovering from a nervous opening against Romania's Elena-Gabriela Ruse to secure a 6-3, 6-2 win at Arthur Ashe Stadium.The third-seeded American needed some time to settle into the match but eventually took control, turning an uncertain start into an 83-minute victory.Pegula entered the final Grand Slam of the season with confidence after reaching the Cincinnati Open final, where she was beaten by fellow American Coco Gauff. Against Ruse, however, the pressure of playing the opening match on the tournament's biggest court was immediately apparent.The 32-year-old failed to convert her first nine break-point opportunities before finally finding her range.Once she did, the match changed quickly.Pegula finds her rhythm after shaky startPegula acknowledged afterward that nerves played a major role during the opening stages.The American said she felt particularly anxious because it was the first round of a Grand Slam, describing her pre-match state as one of intense nervousness.That tension was reflected in her early inability to break Ruse, despite creating repeated opportunities.Pegula eventually settled into her game and began dictating rallies. Her serve became a particularly effective weapon, with the American winning an impressive 92% of her first-serve points during the match.That statistic helped Pegula keep Ruse under pressure while limiting opportunities for the Romanian to build momentum.After taking the first set 6-3, Pegula became increasingly comfortable. She broke away in the second set and closed out the match 6-2, completing a straightforward victory despite the difficult opening.A strong start after Cincinnati finalPegula arrived in New York having enjoyed a productive run in Cincinnati.She reached the final of the WTA event before losing to Coco Gauff, giving her valuable match practice ahead of the US Open.That result also reinforced Pegula's status as one of the leading American contenders in the women's draw.Her opening-round victory in New York now gives her another opportunity to build on that form.The challenge will increase in the next round, however, with Pegula set to face either Venus Williams or Sofia Kenin.Williams and Kenin were scheduled to meet in the final match of the night session at Arthur Ashe Stadium.Venus Williams and Sofia Kenin headline next clashPegula's next opponent will emerge from an all-American matchup carrying plenty of attention.The 46-year-old Venus Williams is competing as a wild card, while Kenin also entered the tournament with wild-card status.Williams remains one of the most recognisable figures in American tennis and has a long history at the US Open. Her presence in New York has added another layer of interest to this year's tournament.The Williams family will have another major storyline at the event as well. Venus is scheduled to partner with her sister Serena Williams in the women's doubles competition.For Pegula, watching the outcome of the Williams-Kenin contest will determine the next challenge in her singles campaign.Jasmine Paolini survives three-set battlePegula was not the only seeded player to advance in the women's draw on Sunday.Jasmine Paolini, the 19th seed, also moved into the next round after a much tougher encounter with Slovenia's Veronika Erjavec.Paolini won 6-3, 3-6, 6-4, needing three sets to overcome her opponent.Unlike Pegula's relatively comfortable finish, Paolini had to withstand a strong response after taking the opening set. Erjavec levelled the contest by winning the second set 6-3, but Paolini recovered in the decider to avoid an upset.Kamilla Rakhimova also progressed, defeating 27th seed Barbora Krejcikova 7-6(4), 6-2.Medvedev and Djokovic take centre stageAttention on the men's side was set to shift toward former US Open champion Daniil Medvedev.The 2021 champion was scheduled to play France's Hugo Gaston at Arthur Ashe Stadium after Pegula's opening match.Medvedev will be looking to rediscover his best form on the hard courts of New York, where he has previously enjoyed some of the biggest moments of his career.But the night's biggest spotlight belongs to Novak Djokovic.The 39-year-old Serbian begins his latest attempt to add another Grand Slam trophy to his record-breaking collection against Argentina's Mariano Navone.Djokovic begins pursuit of 25th Grand SlamDjokovic enters the US Open chasing a record-extending 25th Grand Slam singles title.At 39, the Serbian remains one of the biggest stories of every major tournament, but his preparations for New York have not been entirely smooth.Djokovic was beaten in the opening round of the Cincinnati Open earlier this month, giving his US Open campaign an unexpected element of uncertainty.His experience at Flushing Meadows, however, makes him impossible to overlook.With the top-ranked Jannik Sinner absent from this year's tournament and defending champion Carlos Alcaraz returning after an extended injury layoff, Djokovic has a significant opportunity to make another deep run.Pegula gives home fans an early boostFor American tennis fans, Pegula's victory provided an encouraging beginning to the US Open.Her performance was not flawless, particularly during the opening stages, but the way she recovered from her nerves could prove important as the tournament progresses.Grand Slam campaigns are often decided by how players handle pressure as much as by their shot-making ability. Pegula managed to turn an uncomfortable start into a commanding win, and she will now have time to prepare for another demanding matchup.The US Open is only beginning, but Pegula has already delivered one of the tournament's first reminders that surviving the nerves of opening day can be just as important as playing your best tennis.