After an early exchange of breaks, Sharapova won four consecutive games in the first set and four more in the second. She closed the match on her first match point with a forehand that Fed Cup rookie Soler-Espinosa failed to return.
"I was a bit nervous before the beginning of the match as I failed to show my best tennis in my previous Fed Cup appearance in Moscow," Sharapova said.
Sharapova is playing for Russia for the third time. The three-time Grand Slam champion won both her singles matches against Israel in 2008. She lost in opening singles against France last year.
"It was very important to stay concentrated, to believe and prove that my tennis is better and to win the match," she said. "Luckily, I managed to do all that and now I'm really satisfied with my performance."
Russia has won the Fed Cup title four times since 2004 and is 5-1 against Spain, which won the title five times between 1991 and 1998. The series winner will play Belgium or Serbia in the semifinals on April 21-22.
Kuznetsova won four consecutive games before Suarez Navarro narrowed the gap to 4-3 in the first set. But the two-time major winner won five more games in a row to take a 3-0 lead in the second set. She converted her second match point with a service winner.
"From the scoreline, the match looked easy but in fact it was a bit difficult," Kuznetsova said. "But I've played rather well today and I'm satisfied with my tennis."
In Sunday's reverse singles, Sharapova will face Suarez Navarro, and Kuznetsova will take on Soler-Espinosa. In doubles, Russia's Nadia Petrova and Ekaterina Makarova will play Nuria Llagostera Vives and Arantxa Parra Santonja.
Czech Republic 2, Germany 0
Goerges was two points from winning, leading 5-4 and 30-0 before falling to the second-ranked Kvitova in 2 hours, 21 minutes.
"It was really little difference between us," said Kvitova, who won her 26th straight indoor match.
Benesova served two aces to save two break points while trailing 3-2 in the second set and held serve.
"That was very important," Benesova said. "It gave me a push and I stayed in the match."
The series will be decided Sunday with two reverse singles and a doubles match at Porsche Arena. Germany's 10th-ranked Andrea Petkovic was ruled out with a lower back injury.
This is the seventh meeting between the countries, with the Czechs leading 5-1. The series winner will play Ukraine or Italy in the semifinals April 21-22.
Italy 1, Ukraine 1
Reverse singles and doubles in the first-round, best-of-five series is Sunday.
The 121st-ranked Tsurenko dominated with a big serve and accurate volleys, while Schiavone lacked her usual aggressiveness and fleet footwork.
Errani broke early in each set and was never really challenged by the 89th-ranked Bondarenko. The 34th-ranked Errani usually plays doubles for Italy, but captain Corrado Barazzutti decided to use her in singles because of her results in Australia and Flavia Pennetta's back injury.
"It's never easy to open in Fed Cup but it was a good match, very quick. She was hitting really hard," said Errani. "For me, Fed Cup is the best thing all year."
Italy won the Fed Cup in 2006, 2009 and 2010. But in its previous outing, it played without Schiavone and Pennetta and lost to Russia 5-0 in last year's semfinals, ending its winning streak of eight series. Italy has won all three of its series with Ukraine.
Serbia 1, Belgium 1
Jankovic showed her experience late in the opening set, forcing a first break of serve against the 176th-ranked Flipkens. She went up 4-2 in the second but let Flipkens back in the match. Jankovic saved two set points before winning.
That put the pressure on Wickmayer in the best-of-five series. Wickmayer became Belgium's highest-ranked player after Clijsters lost in the semifinals at the Australian Open title last week. Wickmayer is ranked No. 29 and had enough experience to edge Jovanovski, 76 places below her.
Wickmayer rallied from a 4-2 deficit in the second set but won the final four games.
Information from The Associated Press was used in this report.