"We have won the election," said Transport Minister and UPFA spokesman Dullas Alahaperuma, who predicted the collated results would give his party 138 to 142 seats in the 225-member parliament.
It was the first parliamentary poll since the government defeated Tamil Tiger rebels in May last year, ending a bloody three-decade conflict.
The widely expected victory for the ruling party will further strengthen Rajapakse's grip on power just three months after he won a second term as president by an emphatic margin.
Rajapakse had been hoping for a two thirds majority that would allow him to amend the constitution, which currently limits presidents to two successive terms.
"I want a very strong parliament to develop the country," he told reporters as he cast his ballot Thursday in a southern constituency where his son Namal was the ruling party candidate.
For many Sri Lankans, it was the first legislative election in which they could vote without fear of Tamil Tiger violence and suicide attacks following the defeat of the rebels, which has boosted Rajapakse's standing.
However, the Centre for Monitoring Election Violence (CMEV) reported 286 incidents of violence on polling day, including a shoot out between a group of opposition and government supporters in the south, but nobody was hurt.
There were also numerous reports of pro-government supporters intimidating voters, said the centre's spokesman D.M. Dissanayake.
Another poll monitor said the violence had forced the election commissioner to order a ballot re-run in two of the island's 22 electoral districts, meaning a delay in the formal national result.
Overall turnout was expected to be between 50 and 55 percent of the country's 14 million voters, the lowest ever in a parliamentary poll, after a lacklustre election campaign.
The previous low was 63 percent when Sinhalese militants and Tamil rebels attempted to sabotage the 1989 election by killing dozens of candidates, their supporters and election officials.
While Rajapakse's party should have no trouble securing more than half the 225 seats, Sri Lanka's system of proportional representation makes it unlikely it will secure the two-thirds majority needed to push through constitutional change.
Sethmini Chathurika, 28, said she had voted for Rajapakse's party because it had succeeded in ending the conflict with the Tamil Tigers.
"The president has plans to build the country. I think he deserves a parliament to implement those plans," Chathurika said.
Rajapakse's nationalistic rhetoric appeals to his majority Sinhalese community, but has been criticised by rights groups who accuse him of cronyism and suppressing dissent.
His main election rival, former army chief Sarath Fonseka who led the military campaign that defeated the Tigers, is now in custody and facing court martial.
Opposition parties were largely united behind Fonseka in his campaign for the presidency in January, but they lost cohesion after his arrest and went into the parliamentary election with little hope of victory.
The main opposition UNP had accused the government of using state-owned vehicles and buildings for campaigning and turning the government-run media into a party mouthpiece.