The 35-year-old's Rastriya Swatantra Party (RSP) was also leading in the proportional representation vote, according to results declared and election commission trends.
The vote was the first since deadly September 2025 youth anti-corruption protests toppled the government.
Shah himself had on Saturday defeated the veteran four-time prime minister KP Sharma Oli -- whose Marxist-led government was ousted in the violence last year -- in his own seat.
His victory over the 74-year-old Oli, and his rise from the capital's mayor to potential prime minister, marks one of the most dramatic results in recent Nepali politics.
The September 2025 youth-led demonstrations, under a loose Gen Z banner, began over a brief social media ban but quickly tapped into broader grievances over corruption and a struggling economy.
Elections on Thursday chose a new 275-member House of Representatives, the lower house of parliament, with 185 seats chosen directly, and 110 by a proportional representation vote.
Poll monitors the Asian Network for Free Elections said Sunday that voting had been "peaceful and orderly and reflected continued public engagement with democratic processes despite recent political instability".
- 'Necessary action' -
On Sunday afternoon, 157 of the direct elections had been declared: RSP dominating with 121, Nepali Congress 17, and the Marxists of now-defeated Oli trailing with seven.
Former Maoist guerrilla commander Pushpa Kamal Dahal, a three-time prime minister, won his seat, with his party holding seven in total.
Trends showed Shah's RSP was also leading in half of the remaining eight constituencies in the direct elections.
In the proportional representation vote, RSP was leading with nearly half of the counted votes -- but final results could take several more days.
Nepali Congress, the largest party in the past coalition government, also saw its new leader, Gagan Thapa, defeated by RSP.
"Counting is moving forward smoothly in all remaining constituencies," Election Commission spokesman Narayan Prasad Bhattarai said, adding that final results will take a "few days".
The first-time parliamentary lawmaker Shah toured the streets of his new constituency on Saturday evening, wearing his signature dark sunglasses and waving from the sunroof of a car in a victory parade through cheering crowds who chanted "Balen" -- as he is better known.
Shah, who did not make a speech, won more than three times more votes than Oli, who congratulated the winner, wishing him "a smooth and successful five-year tenure".
Nepal's government-formed investigation commission to probe the deadly September 2025 violence also submitted its report Sunday.
No one has been held accountable for the deaths as yet.
Commission member Bigyan Raj Sharma told reporters the team had questioned more than 200 people, and had submitted a 900-page report -- with more than 8,000 additional pages.
"We tried to conduct fact-finding for September 8 and 9," he said.
"Based on what we saw, understood, and verified through the evidence, we have provided our opinions and recommendations."
The report was handed to Sushila Karki, the interim prime minister.
Karki said it would be up to the new government taking power to act -- but that she hoped its key findings would be made public before she steps down.
"We will not be here for its implementation, because we have to handover to the new government and go," she said.
"But, I believe, that the next government will study and implement this."
Oli has denied ordering security forces to open fire on protesters, and has told AFP that he blames "infiltrators" for the violence.
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