Unified Russia, backed by President Vladimir Putin, is leading in 13 of the 14 regions that voted. The new Kremlin-supported A Just Russia party was ahead in the other region, Stavropol Krai.
The turnout was low (under one-third of the total electorate) and opposition parties say they were sidelined.
The results came as little surprise in an election that is being seen as a test run for federal parliamentary elections in December.
It was a healthy win for the Kremlin-backed Unified Russia party, and a healthy start for A Just Russia, a party positioning itself as the opposition -- despite the fact that it, too, enjoys Kremlin backing.
A Just Russia won outright in one region and was runner-up in many others.
Unified Russia head Boris Gryzlov was confident about his party's success.
"If we speak as a whole about our faction, in nine of 14 regions, we'll have more than 50 percent for the Unified Russia faction," he said. "In the rest, we will have a simple majority [a plurality]."
Opposition Complaints
Most opposition parties performed badly.
Before the vote, opposition parties said they have been sidelined and given virtually no media attention by the Kremlin-controlled media.
Many were barred from running in the regional elections on technical grounds.
In St. Petersburg, the local election commission ruled that the opposition Yabloko party could not run in the ballot for the city's Legislative Assembly. The reason --10.5 percent of the signatures gathered for registration were declared invalid.
Russia's Communist Party (KPRF) leader Gennady Zyuganov was unhappy with the vote, telling reporters there have never been such dirty elections in Russia.
"This is a dress rehearsal before the elections for the State Duma and the presidential election," Zyuganov said. "We'll conduct our own parallel count."
Any evidence of electoral abuses is unlikely to change anything. With the economy performing well, plenty of generous media coverage, and Putin's high popularity, analysts say that Kremlin-backed parties are likely to remain popular with voters.