One-time US Open winner Andy Murray and Stan Wawrinka were among the victors in the first round on Tuesday.
Murray and Wawrinka both won in straight sets to book their spot in the next round.
Juan Martin del Potro, Kei Nishikori and Dominic Thiem were among the other big names to make it through.
However, there were early exits for seeds Bernard Tomic and David Goffin.
MURRAY, WAWRINKA THROUGH
World number two and Olympic gold medallist Murray was largely untroubled by the unseeded Rosol, recording a 6-3 6-2 6-2 win.
Murray, winner at Flushing Meadows in 2012, will face Marcel Granollers in the second round.
Joining him in the last 64 is third seed Wawrinka, who battled past Fernando Verdasco 7-6 (7-4) 6-4 6-4.
TOMIC, GOFFIN ELIMINATED
Tomic and Goffin suffered early exits in New York.
Australian Tomic, the 17th seed, went down to Bosnian Damir Dzumhur, who progressed with a 6-4 6-3 4-6 7-6 (7-0) win.
Meanwhile Goffin, the 12th seed, suffered a 4-6 7-5 6-4 6-0 defeat against 19-year-old local favourite Jared Donaldson.
DEL POTRO, THIEM ENJOY MIXED DAYS
Del Potro - the 2009 US Open winner - and Thiem both made it through to the next round but in contrasting fashion.
Silver medallist at Rio 2016, Del Potro breezed past fellow Argentine Diego Schwartzman with a 6-4 6-4 7-6 (7-3) win.
Austrian eighth seed Thiem, meanwhile, needed just over three hours to see off John Millman 6-3 2-6 5-7 6-4 6-3.
ACE OF SPADES
Ivo Karlovic is renowned for his dangerous serve, but the Croatian took it to the next level on Tuesday. In his five-set thriller against Lu Yen-hsun, Karlovic fired down 61 aces - thrashing the previous US Open record of 49 set by Richard Krajicek in 1999.
Yeah got some shoulder issues https://t.co/NGL0dYs5F8-- ivo karlovic (@ivokarlovic) August 31, 2016
WAWRINKA HAPPY, HECKLER GETS THE BETTER OF TOMIC
"I was really focused on myself. I was moving really well for first one. I'm getting some confidence from that match," - Wawrinka's hard-fought win over Verdasco has him in good stead.
"I'll put my balls in your mouth. I will give you some money to make you feel good," - Tomic was overheard saying as he responded to some heckling from a spectator from the crowd.
"I am so glad to be part of this tournament once again after three years. I really appreciate the wild card who give me to have the chance to play, and that's important for me," said Del Potro after his first victory at the US Open since 2013.
Top seed Novak Djokovic is in action against Jiri Vesely at Arthur Ashe Stadium on Wednesday. The days' action concludes with Rafael Nadal up against Andreas Seppi, while fifth seed Milos Raonic meets Ryan Harrison.