Swiss second seed Federer showed his class against Australia's Marinko Matosevic 6-3 6-4 7-6 (7-4), while Ferrer - the fourth seed of Spain - got past Bosnia-Herzegovina's Damir Dzumhur 6-1 6-2 2-6 6-2 in New York.
Rosol was the only seed to bow out of the men's singles draw on day two at Flushing Meadows, the Czech 29th seed humbled by Croatian upstart Borna Coric 6-4 6-1 6-2.
Coric, 17, flew through his grand-slam debut in one hour 51 minutes, the 2013 junior US Open champion hitting 20 aces in a breathtaking performance.
Japanese 10th seed Kei Nishikori dispatched American wildcard Wayne Odesnik 6-2 6-4 6-2, while France's Richard Gasquet - seeded 12th - was pushed before posting a 7-5 7-6 (7-5) 6-4 triumph over Uzbekistan's Denis Istomin.
American 13th seed John Isner typically needed a couple of tie-breaks as he got past compatriot and wildcard Marcos Giron 7-6 (7-5) 6-2 7-6 (7-2).
There were more straight-sets wins for Italian 15th seed Fabio Fognini and French 26th seed Gilles Simon.
Fognini got the better of Kazakhstan's Andrey Golubev 6-4 6-4 6-2, while Simon downed Moldovan qualifier Radu Albot 6-3 6-4 6-2.
Ivo Karlovic, the Croatian 25th seed, clocked 24 aces on his way past Finland's Jarkko Nieminen 6-4 6-4 3-6 6-4, while French 20th seed Gael Monfils proved too good for American wildcard Jared Donaldson 6-4 6-2 6-4.
Spain's Guillermo Garcia-Lopez, the 28th seed, progressed against Taipei's Lu Yen-hsun 6-4 6-2 6-2, while countryman and 17th seed Roberto Bautista Agut battled to victory over Austrian Andreas Haider-Maurer 5-7 7-6 (7-1) 1-6 7-5 6-1.
Another Spaniard, Marcel Granollers, cruised past out-of-form Austrian Jurgen Melzer 7-6 (7-1) 6-3 6-2, while compatriot Albert Ramos-Vinolas suffered defeat at the hands of Australian Sam Groth, who posted a 6-3 7-6 (7-5) 6-3 victory - his first at grand slam level.
American rising star Jack Sock retired injured after losing the third set to Spain's Pablo Andujar, who advanced when the match ended with him leading 6-4 3-6 6-1.
Sam Querrey, though, advanced for the local contingent, scraping his way to a tough win against Argentine Maximo Gonzalez 6-2 4-6 6-4 4-6 6-3, while Tim Smyczek also pleased the fans out on Court Five with a 4-6 6-3 6-2 7-6 (7-5) triumph against Serbia's Filip Krajinovic.
Australia's Bernard Tomic saw off the threat of Germany's Dustin Brown 7-6 (7-2) 6-4 7-6 (7-3), and will meet Ferrer in the second round.
Federico Delbonis of Argentina saw off American teenager Noah Rubin 6-4 6-3 6-0, while Paolo Lorenzi of Italy progressed when his opponent, Japanese qualifier Yoshihito Nishioka, retired injured with the score 6-1 6-2 2-1 in Lorenzi's favour.
Colombia's Alejandro Gonzalez had too much touch for the returning Dmitry Tursunov winning 6-4 6-4 7-5 over the Russian, who has not been in action since Wimbledon.
Dominican Republic's Victor Estrella Burgos chalked up his career first grand-slam level win at the ripe old age of 34, downing Dutchman Igor Sijsling 2-6 6-4 6-3 6-2.
Germany's Jan-Lennard Struff came from two sets down to dismiss Kazakhstan's Mikhail Kukushkin 2-6 3-6 6-3 6-3 7-5, while French lefty Adrian Mannarino also arrested a deficit to progress past Spain's Pere Riba 3-6 7-5 6-3 6-2.