Sharapova became the first woman into the third round at the U.S. Open by using 12 aces to help set aside a poor start and coming back to beat Timea Babos of Hungary 6-7 (4), 6-4, 6-1.
Roger Federer, meanwhile, shrugged when asked about the noise after his five-set victory over American teenager Frances Tiafoe.
Angelique Kerber's exit further thins the women's bracket, which was missing 23-time major champion Serena Williams to begin with because she is expecting a baby.
Roger Federer had to overcome an early deficit and a late lapse Tuesday night to edge 19-year-old American Frances Tiafoe 4-6, 6-2, 6-1, 1-6, 6-4 in a compelling first-round contest.
Maria Sharapova recovered after faltering midway through the match and emerged to beat Simona Halep 6-4, 4-6, 6-3.
Andy Murray, who yielded the No.1 ranking to Rafael Nadal this week, has not played a match since July 12 at Wimbledon.
Ajay Jayaram, seeded 13th, produced another clinical show to get past world No. 50 Mark Caljouw 21-13, 21-18 in a 33-minute men's singles match.
Milos Raonic joins 12-time major champion Novak Djokovic, 2016 US Open champion Stan Wawrinka and 2014 finalist Kei Nishikori in missing the tournament because of injuries.
Ramkumar, now India's number one singles player at 156, faces seasoned Frenchman Paul-Henri Mathieu, who is now placed 213 in the ATP ranking chart.
Petra Kvitova, a two-time Wimbledon champion, lost 6-2, 6-1 in the first round.
Victoria Azarenka has not played since Wimbledon, and the former No. 1 player is now ranked 204th.
Murray, who was out of action because of a hip injury, drops to second spot with 7,150 points.
Garbine Muguruza defeated Simona Halep 6-1, 6-0 for her first Western & Southern Open title on Sunday, needing only 56 minutes to extend her run of success.
Halep will become World No.1 for the first time if she can defeat Muguruza to capture her maiden title in Cincinnati.
Nadal was sloppy at the outset and on the defensive for much of a 6-2, 7-5 loss that lasted an hour and 20 minutes.
Rohan Bopanna and his Croatian partner Ivan Dodig lost 1-6, 7-6, 7-10 to second seeds Lukasz Kubot of Poland and Marcelo Melo in an enthralling three-setter quarterfinal.
U.S. Tennis Association announced the 33-year old Australian's withdrawal because of an injured right hand on Friday.
Wimbledon champion Garbine Muguruza overcame a long rain delay in the third set and fought off three-match points before advancing to the quarterfinals at the Western & Southern Open.
Rohan Bopanna and Ivan Dodig rallied to humble the pair of Juan Sebastian Cabal and Fabio Fognini 5-7, 7-5, 10-8 in a second round match.
This was Ramanathan's second consecutive defeat against the American, having lost to him in the second round of the Roland Garros Qualifier in 2015.
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