Safina gave Russia an early lead by beating Alize Cornet 6-3, 6-2, but Gilles Simon then defeated Safin 7-6 (5), 6-3. In mixed doubles, Russia beat France 6-4, 6-3, its third straight win in the round-robin format this week.
France had a chance to make Friday's final, but needed to beat Russia in straight sets. Once the French lost the first set, only Russia and Italy had a chance to advance.
"It was hard after we lost the first,'' said Cornet. "But they were a better combination tonight.''
Safina and Safin fell behind 4-1 on two service breaks before mounting a comeback, but not before a few words and glares were exchanged between the siblings on court.
"It's a brother-sister relationship,'' Safin said, grinning. "I think we all know about that.''
"It was good getting through,'' added Safina, "or it could have been the first and last time we played together.''
Italy beat Taiwan 3-0 in another Group B match Thursday, but Flavia Pennetta's 7-5, 6-3, win over Hsieh Su-wei in women's singles was the only completed match. Simone Bolelli won the singles and Italy the mixed doubles when Lu Yen-hsun couldn't take the court due to a quadricep injury, giving Italy both matches on walkovers.
Slovakia, also 3-0, advanced earlier when Dominika Cibulkova and Dominik Hrbaty won their singles matches over Germany, aided by an injury to Nicolas Kiefer.
Cibulkova beat Sabine Lisicki 7-6 (3), 6-4 in women's singles. Hrbaty was then trailing 3-1 in the opening set and Kiefer was serving and one point away from taking a 4-1 lead when the German turned his right ankle.
Unable to continue, Kiefer, 31, had his ankle heavily taped and was taken off the court in a wheelchair. He suffered ligament damage and his availability for the Australian Open which begins Jan. 19 is uncertain.
In the other Group A match Thursday, the United States beat Australia 2-1. It was the first win after two opening losses for the Americans, while Australia finished 0-3.
Casey Dellacqua beat American Meghann Shaughnessy 6-3, 6-4 and James Blake beat Australian Lleyton Hewitt 6-2, 6-2 in a match in which Hewitt, making his return after five months off with a hip injury and surgery, was bothered by an ear infection.
Shaughnessy and Blake defeated Dellacqua and Hewitt 6-3, 5-7, 10-6 (match tiebreak) in mixed doubles, with Hewitt double-faulting on match point.
"It was not the Lleyton Hewitt of old, he was not at his best,'' Blake said after the singles match. "I hope he's healthy for the Australian Open.''
Slovakia beats United States at Hopman Cup
US loses to Germany at Hopman Cup
Guardiola Pleased Yet Sad With Barcelona Defeat
Del Nido: Sevilla Can Beat Real Madrid At The Bernabeu
