The prime minister's governing alliance had about 57 percent of seats in the 452-seat legislature, according to a poll published after elections on national television TVR.
Coming in second was a center-right group, allied to President Traian Basescu, which polled over 18 percent. A populist party headed by a media tycoon won about 13 percent, according to the poll. First results are expected Monday.
Basescu and Ponta are bitter rivals after the government tried to remove Basescu from office in an impeachment vote in July, a bid that failed as too few people voted to make the election valid.
Basescu has indicated he won't appoint the 40-year-old Ponta again, calling him a "compulsive liar" and saying he plagiarized his doctoral thesis. Ponta says Basescu is a divisive figure who overstepped his role as president by meddling in government business.
"We won a clear majority, a majority recognized by our adversaries who have to accept the rules of democracy," Ponta said after the vote. "I assure them we will treat the opposition with the respect that we did not get when we were in opposition."
Ponta became prime minister in May, the third prime minister this year, but his appointment brought a bitter battle with Basescu, whose mandate expires in 2014.
Basescu could nominate someone else, but his choice would have to be approved by Parliament. If his candidate fails in two rounds of voting, Parliament could be dissolved.
As he voted, Basescu again accused the government of the former communist country of failing to devote itself to democratic reforms. He said Romania must continue its "path toward the West" and show the world it is "headed toward Brussels, not Moscow, and Washington, not Beijing."
For his part, Ponta said he remains committed to leading Romania to a better future.
Many Romanians are fed up with the power struggle between the top two leaders, especially as the country remains one of the poorest and most corrupt members of the European Union. Romania is enduring deep austerity cuts in return for a (EURO)20 million ($26 million) bailout to help its foundering economy.
Sunday's vote was hampered by heavy snow and authorities asked the army and the defense ministry to help clear roads closed by blizzards. About 250 polling stations were prevented from opening on time, officials said. Turnout was more than 30 percent three hours before the polls closed.
Heavy rain was falling in Bucharest early Sunday, but it eased off later.
Valentina Lupan, an architect voting in Bucharest, said she was determined to cast a ballot, despite the bad weather.
"People will go and vote even if there's snow and rain because they've had enough," she said. "We've had enough of being insulted and humiliated. We want a normal life."
Besides the failed bid to impeach Basescu, the country has seen three prime ministers and Cabinets this year and huge anti-austerity protests. The EU and the U.S. criticized the government for failing to respect the rule of law and of ignoring constitutional rules during the impeachment attempt.
The Organization for Security and Cooperation in Europe monitored Sunday's vote.