Furlan, ranked 84th in the world, inflicted a 3-6, 6-3, 6-4, 3-6, 6-3 defeat on Enqvist, who has slipped to 15th in the world rankings after a series of injuries and illnesses.
Earlier, Jonas Bjorkman, the highest-ranked Swede at 13th in the world, lost a first-set tie-break to Omar Camporese and had to work hard against the veteran Italian to earn a 6-7, 6-3, 6-2, 3-6, 6-3 victory in the day's opening encounter.
Bjorkman and Nicklas Kulti, doubles finalists at the US Open, meet Camporese and Diego Nargiso in today's doubles.
In the other semi-final in Washington, Michael Chang gave the United States a 1-0 lead against Australia after he beat Patrick Rafter 6-4, 1-6, 6-3, 6-4.
Boris Becker blasted his way past Luis Herrera in straight sets to give Germany a 1-0 lead over Mexico in their World Group qualifying round in Essen.
Becker, who won 7-5, 6-2, 6-3, needed just two hours to beat the Mexican. He used the fast indoor carpet surface to his full advantage.
Becker broke for a 6-5 lead in the first set and then went on to win the next six games, in the process closing the first set 7-5 and taking a 5-0 in the second.
"I had trouble reading his serve at the beginning. But once I broke him, I took control," Becker, who had wasted two break points in the seventh game, said.
The three-times Wimbledon champion cruised to hold a 5-2 lead in the third set. He dropped his serve while serving for the match but broke right back to put Germany ahead.
"I lost my concentration a bit at the end," said Becker, who has announced his retirement from Grand Slam singles play.
Becker had not played competitively since injuring himself at a tournament in Stuttgart in July. He missed the US Open because of the death of his manager.
In another qualilfying round match in Harare, Thomas Muster and Byron Black had little trouble in their opening singles matches to leave Zimbabwe and Austria level at 1-1.
Black beat the Austrian No 2, Gilbert Schaller, in straight sets 6-3, 6-2, 6-1. Muster's all- around power was too much for Black's younger brother Wayne, and he won 6-3, 6-0, 6-4.
Muster served 10 aces in overwhelming the second-ranked Zimbabwean, also using cross-court forehand passes to great effect.Reuse content