Virginie Razzano defeated Sharapova 6-3, 6-4 after Alize Cornet rallied to beat Kuznetsova 3-6, 6-3, 6-4. Reverse singles and a doubles match will be Sunday in the best-of-five series.
A set and 4-1 down, Sharapova won three consecutive games to even it 4-4. But Razzano broke for a 5-4 lead and served out the match at love.
"Unfortunately we've lost two matches today," Sharapova said. "I tried to fight for every ball today but it didn't work. We both had chances in our matches and it seemed we'd found our games, but then it all vanished."
Sharapova played her first home Fed Cup match for Russia. She won both singles in her Fed Cup debut against Israel in 2008.
Sharapova had defeated Razzano in the second round of the Australian Open. The Frenchwoman learned from the loss.
"The key for my victory was that I put pressure on her on her serve," Razzano said. "And she felt that pressure throughout the whole match. A low percentage of her first serve speaks to it."
Sharapova put in only 30 of 53 first serves and had eight double-faults.
The 67th-ranked Cornet was a set and 2-0 down when she tied it 2-2 in the second set and broke Kuznetsova in the eighth game. After trading breaks three times in the third set, Cornet broke for a 5-4 lead and served the match out with a forehand cross-court winner.
"I didn't feel that I would win," Cornet said. "I just tried to fight for every point. And just at the match point, when I finally made the winner and won the match, I realized what I'd done — and that was a great moment."
Serving at 40-30 in the fourth game of the third set, Cornet stumbled and appeared to have twisted her right ankle. She took a medical time out and had her ankle bandaged.
"I really twisted my ankle and it was very painful at the moment," Cornet said. "But with the tension and the motivation that I was feeling on the court, I just tried to forget about the pain."
Kuznetsova said the injury didn't seem to slow Cornet.
"It's always hard to play someone who is injured," Kuznetsova said. "But in the end, I understood that nothing mattered — she moved the same way as before."
The 23rd-ranked Russian had 62 unforced errors and converted only five of 16 breakpoints.
"I have no excuses," Kuznetsova said. "I've lost a match that I should have won, in any case. I opened strongly but then started to hurry and do strange things, and that's the result of it."
Sharapova said Russia had not lost yet.
"There will be a new day tomorrow and new struggle," Sharapova said. "We have the whole day ahead and we'll do our best."
In Sunday's first reverse singles, Sharapova was drawn to play Cornet. In the second match, Kuznetsova was to face Razzano. However, reverse singles and the doubles players are subject to change.
The winner of the match will play either Australia or Italy in the semifinals on April 16-17.