Venus Williams, a wild-card entry, fell to Sabine Lisicki of Germany 6-1, 6-2. Lisicki didn't face a break point and broke Williams three times.
Djokovic's run of 100 weeks at the top of the ATP rankings is in danger this week from Rafael Nadal, who defeated Santiago Giraldo of Colombia 6-2, 6-4. Nadal will take the No. 1 spot if he reaches the final.
Djokovic will play Fernando Verdasco in the second round after the Spaniard beat Indian qualifier Somdev Devvarman 7-6 (6), 6-3. Nadal's second-round opponent will be Philipp Kohlschreiber of Germany.
Serena Williams, who lost only one game in a win over Schiavone at the U.S. Open, had a much tougher time against the Italian this time. Schiavone held three set points at 5-3 in the second set, but Williams won 15 of the last 17 points to close out the match.
"It didn't surprise me," Williams said. "I was definitely more surprised that I played so well in the Open, but it was a different circumstance -- even though the score line looked much easier at the Open, it wasn't an easy match. But as for Francesca playing so well today, I wasn't surprised about that."
In other men's matches. fifth-seeded Richard Gasquet beat Florian Mayer 6-3, 7-6 (2); No. 6 Stanislas Wawrinka of Switzerland overcame Andreas Seppi 4-6, 6-3, 6-4, and No. 8 John Isner came back to down China's Di Wu 5-7, 7-6 (4), 6-3.
Former women's No. 1 Caroline Wozniacki beat Monica Niculescu of Romania 6-3, 6-1 to remain on course to face Serena Williams in the quarterfinals.