NEW YORK, Aug 30 (Reuters) - Simona Halep, who missed three of the year"s biggest events while recovering from a calf injury, delivered a statement win on her return to Grand Slam action when she beat Italian Camila Giorgi 6-4 7-6(3) on Monday to reach the U.S. Open second round. The former world number one, who is seeded 12th in New York, relied on a solid serving game to get by the in-form Giorgi, who won the biggest title of her career two weeks ago in Montreal. Halep twice failed to serve out the win but the Romanian, staring at the possibility of having to play a decider, regained control of the match and breezed through the tiebreak. "At 5-4 (in the second set) I felt the pressure. Because I don"t have many matches, I felt sick a little bit because I knew actually I have to finish the match because in three sets would be a little bit tougher," said Halep. "But, you know, I"m happy that I can see my serve improving, and I can win some easy points with it. So I have been looking for it many years, but now finally I can feel it stronger." Halep missed the French Open, Wimbledon and the Tokyo Olympics due to an injury suffered in Rome and then, in only her second tournament back, was forced to withdraw from a U.S. Open tune-up event in Cincinnati due to a right thigh injury. The 29-year-old Romanian was considered to be one of the more vulnerable seeds in New York but showed she was up for the task at hand in the day"s first match on Grandstand. Halep, a two-times Grand Slam champion whose best U.S. Open finish came in 2015 when she reached the semi-finals, won 83% of her first-serve points, fired down six aces and faced just two break points during the 93-minute match. "I knew she had confidence, I knew she"s playing super fast and deep, so I had to be strong on my legs. I"m struggling with the legs lately," said Halep. "But, you know, I think I have been very positive on court. I have been very, you know, like confident that I have the game to play a good match, and I believed that I have a chance. "So I fought for it, and I"m pleased with the way I handled the important moments." Next up for Halep will be Slovakian lucky loser Kristina Kucova.