My Step Alliance, which includes Pashinyan's Civil Contract Party, won 70.4 percent of the vote based on results from all polling stations, the Central Election Commission (CEC) said on its website.
Results showed that two moderate opposition parties - Prosperous Armenia and Bright Armenia - got enough votes to clear the 5 percent threshold to enter parliament.
Nine political parties and two electoral blocs were competing for mandates in the 101-seat National Assembly.
More than 2.6 million people were eligible to vote in the election monitored by international observers from the Organization for Security and Co-operation in Europe.
Pashinyan came to power in Armenia in May after weeks of mass protests against corruption and cronyism that was dubbed the "velvet revolution".
The former newspaper editor, who was jailed for fomenting unrest in 2008, marked a dramatic break from the cadre of rulers who have run Armenia since the late 1990s.
He stepped down in October so parliament could be dissolved for the early election but remained the acting prime minister.
"Armenian citizens created a revolutionary majority at the parliament," Pashinyan told reporters at his bloc's headquarters after first results were published.
"If this trend continues, the majority won't face any problems in implementing legislative changes," he said.
After a change of power in the South Caucasus country of around three million people, Pashinyan's government sought to initiate changes to the electoral code. But the move was blocked by the former ruling Republican Party, which dominated parliament.
'An extraordinary accomplishment'
Reporting from the capital Yerevan, Al Jazeera's Robin Forestier-Walker said that Armenia is now in a new place and the question is whether Pashinyan can deliver on the reforms and changes which are going to be extremely challenging.
"It's an extraordinary accomplishment when you see that the Republican Party, the party of government for the past two decades failed to pick up, it seems, even a single seat," Walker said.
"In fact they sabotaged their own possibility of clinging on and being still a viable political force when he, Nikol Pashinyan, tried to introduce electoral reforms that would have reduced the threshold, they blocked him. If they hadn't blocked him, they still would have some potential seats in parliament."
The Republican Party received 4.7 percent of the vote and it was not clear whether it managed to enter parliament. Under Armenia's constitution, 30 percent of seats in parliament must go to opposition parties.
Former high-ranking officials were sacked and some were arrested following the change of power. An appeals court ordered the detention of former President Robert Kocharyan on Friday on charges of attempting to overthrow the constitutional order.
He was first arrested in July but freed the following month and the case was sent to the appeals court. Kocharyan was Armenia's second president, serving from 1998 to 2008, when mass protests erupted over a disputed election.
Pashinyan promised after taking office there would be no major shifts in Armenian foreign policy and has offered assurances he will not break with Moscow.
Forestier-Walker said that Armenia faces many foreign policy challenges as well as poverty and corruption on the domestic front.
"Armenia is surrounded by two hostile neighbours - on the one side Azerbaijan to the east with the ongoing conflict over the Karabakh region. To the west, with Turkey which has closed its borders to Armenia over that ongoing dispute with Azerbaijan," Forestier-Walker said.
"Russia is the lifeline to the north and Armenia will still continue to depend on Russia for its security.
"Iran to the south, with the Americans of course restricting with new sanctions; that's a problem for Armenia. Armenia had quite good ties with Iran."