The top-seeded Spaniard needed just 43 minutes to advance and next plays Frenchman Benoit Paire, who beat Ito Tatsuma of Japan 6-3, 7-5. Sijsling won only one game in front of his home crowd at the grass-court tournament.
It was Clijsters' third win of the tournament, providing a boost after she had been sidelined most of the season due to injuries. She next plays Urszula Radwanska of Poland, who defeated Sofia Arvidsson of Sweden, 6-2, 7-6 (3).
Clijsters will play in Wimbledon, but is unseeded at the Grand Slam tournament that starts on Monday.
"It was a very intense match. Schiavone is a player who keeps fighting and has all sorts of different strokes," Clijsters said.