Sharapova, playing her first Fed Cup match in three years, had crumbled to a 6-3, 6-4 defeat to Virginie Razzano on Saturday in her opening singles rubber and did not feature in Moscow on Sunday.
Russia had been 2-0 down overnight after Alize Cornet had seen off Svetlana Kuznetsova 3-6, 6-3, 6-4.
But on Sunday, 19-year-old, world number 14 Pavlyuchenkova defeated Cornet 3-6, 6-3, 6-2 before Kuznetsova levelled the World Group I clash by seeing off Razzano 6-4, 6-4.
No team had ever overturned a 2-0 deficit in the history of the event, but Pavlyuchenkova ignored the record books to partner Kuznetsova to a 7-6, (7/4), 6-0 win over Cornet and Julie Coin in the decisive doubles.
Russia, the 2004, 2005, 2007 and 2008 winners, will now face two-time defending champions Italy at home in the semi-finals in April.
"I found out on Saturday that I was playing. At the draw, we decided to see how it went on the first day and then we'd decide," said Pavlyuchenkova.
Italy completed a 4-1 rout of Australia in Hobart with world number Flavia Pennetta extending her winning streak in the competition to 10 matches with a 6-3, 6-2 triumph over Jarmila Groth.
That followed world number four, and French Open champion, Francesca Schiavone's 7-6 (7/1), 3-6, 7-5 win over fifth-ranked Samantha Stosur.
Roberta Vinci and Sara Errani saved two match points to fight back and beat the Australian combination of Rennae Stubbs and Anastasia Rodionova, 2-6, 7-6 (7/1), 6-4 in the dead doubles rubber.
"We are really happy about this match (result). It was really tough for everyone here," Pennetta said.
Australian Open champion Kim Clijsters secured Belgium's ticket for the semi-finals thanks to a 6-7 (10/12), 6-2, 6-1 victory over Bethanie Mattek-Sands in Antwerp as the home side took an unassailable 3-0 lead over the United States.
Yanina Wickmayer breezed past Melanie Oudin 6-2, 6-0 to make it 4-0.
"I was expecting (a tough match) when I came out at the start," said Clijsters, who was part of the Belgian side which won the Fed Cup a decade ago. "I played her a few months ago, and she played a really tough match, you know a very high level and she did that in the first set today as well."
Belgium will tackle the Czech Republic, who saw off neighbours Slovakia 3-2 in Bratislava, for a place in the final.
The Czechs reached their third successive semi-final after Petra Kvitova, the world number 18, swept aside Daniela Hantuchova 6-4, 6-2 in the first of Sunday's reverse singles to grab the key third point.