Top seed Williams needed just 30 minutes to begin her bid for a first calendar Grand Slam as Vitalia Diatchenko retired at 6-2 2-0 down.
Nadal, seeded eighth, saw off 18-year-old Borna Coric 6-3 6-2 4-6 6-4. World number one Novak Djokovic went through, but fourth seed Kei Nishikori was beaten.
