Russian second seed Anna Chakvetadze beat Israeli Shahar Peer 6-3 6-4 and plays the winner of Thursday's second-round match between Frenchsixth seed Marion Bartoli and Britain's Anne Keothavong.
Griffin (3-2) serenaded his teammates in the visiting clubhouse with guitar and song in English, Spanish and French before preparing for his sixth start of the season.
The Spaniard beat his Swiss rival in the final of the French Open and also denied Federer a sixth consecutive Wimbledon title with victory in the final at the All England Club in July.
The euro slid for a sixth day versus the dollar after French Socialist Francois Hollande was elected president and Greek voters picked anti-bailout parties.
Laura Collett, who topped the standings on Friday on her Badminton debut, lies in sixth place on Rayef behind Piggy French and Jakata, with New Zealand's Andrew Nicholson fourth with Nereo.
Nadal's victory here last year came in Djokovic's absence, and the Spaniard subsequently lost to him in Madrid and Rome before beating Roger Federer in the French Open final for a record-equaling sixth title at Roland Garros.
Cilic was joined in round three by French fifth seed Jo-Wilfried Tsonga and Spanish sixth seed Fernando Verdasco, who both recorded straight-sets victories.