It won 29.4% of the vote, according to the final tally from Swiss broadcaster SRF, up from 26.6% in the 2011 vote and far exceeding expectations. It was the best performance by a party in at least a century, the report says.
This translated to an extra 11 seats in Switzerland's lower house of parliament to bring its tally to 65, the highest for any party since the chamber's membership rose to 200 in 1963.
Success for the SVP, coupled with gains made by the pro-business Liberal Party (FDP), led political commentators to talk of a "Rechtsrutsch" - a "slide to the right" - in Swiss politics.
Immigration was the central topic for voters amid a rush of asylum seekers from the Middle East and North Africa to Europe.
"The vote was clear," SVP leader Toni Brunner told Swiss television. "The people are worried about mass migration to Europe."
Sunday's result cemented the SVP's position as the dominant force in Swiss politics.
The election gains for the SVP, which was already Switzerland's biggest single party, come 20 months after the Swiss in a referendum backed limits on foreigners living in the Alpine nation. The SVP had strongly supported the restrictions.
The left-leaning Social Democrats (SP) finished in second place. Their share of the vote rose 0.1 percentage points to 18.9% but they were set to lose three seats, according to SRF.
The FDP, Switzerland's third largest party, saw its support edge up 1.3 points and was seen gaining three extra seats, tilting parliament further to the right.
The SVP and FDP benefited from a drop in support for the centrist BDP and the two green parties.
In Switzerland's 46-member upper house, 19 races are still open and will be decided in run-off elections. In the votes in so far, the SP was seen losing five seats to have a total of six.
The SVP, currently the upper house's fourth-biggest block, was seen keeping its five seats but had yet to make any gains.
During the election campaign, the SVP rallied against Swiss reforms to deal with asylum seekers, even though in Europe's current migrant crisis Switzerland is handling far fewer migrants than some other nations such as Germany.
