Federer never appeared threatened by the 76th-ranked Matosevic, although he did threaten to take a set off the five-time US Open champion.
Federer won 6-3 6-4 7-6, with the the third set decided in a tiebreaker.
Serena Williams quest to join Chris Evert and Martina Navratilova in joint fourth place on the career grand slam list began with an easy 6-3 6-1 victory over 18-year-old fellow American Taylor Townsend.
Williams, seeking her third successive US Open title and 18th grand slam singles crown of her career, was simply too experienced for the erratic-yet-gifted Townsend, the 2012 Australian Open junior singles and doubles champion.
Margaret Court with 24 titles, Steffi Graf with 22 and Helen Wills Moody with 19 lead the list of all-time grand slam singles titles in women's tennis.