The top-seed and world No 3, was playing for his first time since losing to Peter Sampras, the world No 1, in the Grand Slam Cup final two weeks ago.
Rafter became the second player in the top 10 to lose to Clement recently. The Frenchman beat Spain's Sergi Bruguera, No 8 in the world, last week in Vienna before losing to the former Wimbledon champion, Dutchman Richard Krajicek.
The Frenchman was ranked just 136th in the world last week but he will now move into the top 100 after his two big victories.
He faces the winner of a battle between two more Frenchmen, the Wimbledon finalist Cedric Pioline and another wild card, Sebastien Grosjean.
In other first-round matches, Krajicek, seeded sixth here, defeated Morocco's Hicham Arazi; the American Todd Martin defeated another Frenchmen, Olivier Mutis, 6-2, 7-6 and Mark Philippoussis of Australia, seeded seventh, outlasted yet another French player, Nicolas Thomann, 7-6 4-6, 6-3.
Felix Mantilla, the fourth seed from Spain, won when Andrei Medvedev of Ukraine had to retire with an injury in the second set of their match.
Britain's Tim Henman, who lost to compatriot Greg Rusedski in Sunday's final of the Vienna Trophy, plays his first-round match with France's Guillaume Raoux tonight.