Li, 24, who became the first Chinese player to reach a Grand Slam quarter-final this month, eased past Kristina Barrois 6-3, 6-4 in 74 minutes.

Zheng, who claimed China's first Wimbledon title with doubles partner Yan Zi, beat Kathrin Woerle 6-4, 7-5.

Li said her confidence had been boosted by her performance in London, where Kim Clijsters eventually ousted her.

"I was playing at home and after Wimbledon my confidence increased a lot. Every match I try my best to win," said Li.

She added that the Fed Cup play-off was more important than the WTA tour, because she was "playing for her nation, not for herself".

Barrois, ranked 129 to Li's 22, questioned the quality of the refereeing which she said favoured the Chinese player.

"I think I played not bad but Li played very well," said Barrois.

"I think the referee was not on my side. Li was playing at home, and it was not easy for me. But I did my best."

Meanwhile Zheng recovered from 4-2 down in the first set to beat Woerle, ranked more than 100 places below her at 154th, earning the winning break at 6-5 in the second.

"I didn't play very aggressive and she was a very good player. She served well and she took her chance."

Entry into the eight-nation World Group would mark another success for China whose women have been making great strides in recent years.