Rafter came back from two sets down to beat Cedric Pioline 3-6, 6-7, 6-4, 7-5, 6-4 in four hours and 15 minutes on the White City grass court where temperatures reached 36C.
The results left France facing the prospect of a first-round defeat only nine weeks after their thrilling 3-2 victory over Sweden in the 1996 cup final.
"We've been there before and we have to dig deep again and come back," said the French captain, Yannick Noah, whose team recovered from 2-0 down against the Swedes to win the final.
But Australia, back in the World Group after two years in regional competition, are confident of wrapping up the tie in today's doubles.
Their doubles pair, Mark Woodforde and Todd Woodbridge, are the most successful pair on the circuit and are the reigning Wimbledon, US, Australian and Olympic champions.
Woodforde is also playing singles. He raced past an out-of-sorts Arnaud Boetsch 6-4, 6-4 6-3 in just 97 minutes yesterday.
Carlos Moya, the Australian Open finalist, scored a straight-sets victory over Marc Goellner to give Spain the lead over Germany in another World Group first-round tie in Majorca yesterday.
Moya, playing in his first match in Spain since reaching the Melbourne final, won 6-4, 6-3, 6-3 in one hour 40 minutes on a specially prepared clay court. Albert Costa then made it 2-0 to Spain by defeating Hendrik Dreekman 6- 4, 6-1, 6-4