United Russia, backed by President Vladimir Putin, is far ahead in the nation's parliamentary election, taking at least 44%, exit polls suggest.
Mr Putin said: "We can say with certainty that the party has achieved a very good result."
The nationalist LDPR and the Communist party are way behind United Russia, with about 14-16% each.
Liberal opposition parties appear to have failed to pass the 5% threshold needed for party-list representation.
However, the exit polls say though they could still get seats in individual constituencies.
A VTsIOM exit poll gave United Russia, led by Prime Minister Dmitry Medvedev, 44.5%, with the Public Opinion Foundation putting its total higher, at 48.7%.
Partial official results later confirmed a large lead.
The two exit polls differed on whether the LDPR or Communists were second, but both were well behind.
A Just Russia was fourth on about 8%.
These four parties had dominated the last State Duma (lower house).
Two opposition parties, Yabloko and Parnas, were projected to receive 3.5 and 1.2% respectively.
The turnout was significantly down from the 2011 elections - just below 40% two hours before voting ended.
Election Commission head Ella Pamfilova said she was "fully confident that the elections are proceeding in a quite legitimate way".
Legitimate vote? By Steve Rosenberg, BBC News, Moscow
In the system of "Managed Democracy" crafted by the Kremlin, it was unthinkable that President Putin's control of parliament would weaken.
And so, the four pro-Kremlin parties which dominated the previous parliament will do so again. But will the new parliament be recognised by the public as legitimate?
The Russian authorities have tried to present this as one of the cleanest elections in years. Some opposition candidates were permitted to run; a respected human rights advocate was appointed head of the Russian Election Commission.
Yet throughout the day there have been reports of voting fraud - and video to back them up. In some cases, webcams installed at polling stations recorded what appear to be election officials stuffing ballot boxes.
It was vote-rigging which sparked anti-government street protests after the last parliamentary election. President Putin will be hoping that this time his personal popularity, combined with widespread apathy, will mean that Russians accept the result.
Allegations of fraud after the last election had sparked large-scale protests against Mr Putin in Moscow and the authorities were anxious to oversee trouble-free polls this time.
Mr Putin has enjoyed 17 years in power as either president or prime minister, and does not belong to any designated party.
But he visited the headquarters of United Russia with Mr Medvedev after the vote to congratulate activists on their victory.
"We know that life is hard for people, there are lots of problems, lots of unresolved problems," Mr Putin said. "Nevertheless, we have this result."
Crimea votes
Voters were choosing 450 MPs in the State Duma for the next five years.
But despite Russia's economic malaise and tensions with the West over the conflicts in Ukraine and Syria, some observers had called the election campaign the dullest in recent memory.
Serious irregularities were reported in one Siberian region, with suggestions of "carousel" voting - people bussed around polling stations - in the city of Barnaul.
Monitoring group Golos says it had received more than 1,300 complaints from around the country by late afternoon, AP reports.
For the first time, people voted in Crimea, annexed from Ukraine in 2014 in a move condemned internationally.