Interim data at 1630 GMT showed voter turnout at 68.13 percent, exceeding final turnout in the past three elections.
Polling stations throughout Hungary have officially closed, but authorities have said they are allowing the last few voters who lined up before the 7 p.m. deadline (1700 UTC) to cast their vote.
Voting at the same polling station, kindergarten nurse Szilvia Nagy said: "I would like to change the government, because I desire a nicer future".
Preliminary results from the National Election Office have Fidesz winning Sunday's parliamentary election with 49.5 percent of the vote.
"It's for sure that a low turnout would only have favoured Fidesz" and its highly committed voters, said Gabor Gyori, a senior analyst at political research institute Policy Solutions.
Winning another two-thirds majority would give Orban the chance to boost a new class of politically-connected oligarchs, tighten his grip on institutions such as the courts, and strengthen resistance against countries like France and Germany that are seeking to deepen European Union integration.
"We are celebrating democracy and it seems like this feast will be lovely because many of us are taking part", said Gergely Karacsony, the leading candidate of the left-wing Socialist and Dialogue parties. The outcome could affect the unity of the European Union.
"Theoretically everything is still possible as we don't know the data yet. but in Hungary a two-thirds victory is possible if neither side loses more than 10 districts and there is a difference of at least 20 percent between the victor and the runner-up", Gulyas said.
Polls predicted the triumph of Orban's Fidesz party and its allied Christian Democratic People's Party (KDNP).
High turnout may ultimately also hurt smaller opposition parties, because it would raise the number of votes needed to reach the 5 percent threshold to get into parliament.
Hungarian election officials say voter turnout in the country's parliamentary election 90 minutes before polls close has already exceeded the total turnout for the 2014 elections. "This means either an overwhelming support for Orban or the end of Fidesz as (the) omnipotent political party in Hungary".
On Origo.hu, a formerly independent website now owned by government allies, stories promoted Orban while also focusing on migration with headlines like "Migrant gangs fought in England", "They can't stand it anymore in Sweden: They've had enough of migrants", and "A migrant in underpants beat a German retiree half to death".
The leader of Hungary's right-wing nationalist Jobbik party says he expects a "surprise" result in the parliamentary elections.
Uncertainties about Orban's expected margin of victory are caused by Hungary's complex electoral system in which voters cast two ballots, one for an individual candidate in their region and another for a party list.
Attention is focused on how much support the opposition bloc can win. Another 93 seats will be distributed based on votes for entire party lists.