The government collapsed after a video showed long-time leader of the Freedom Party, Heinz-Christian Strache, appearing to offer favours to a purported Russian investor.
Exit polls released by public broadcaster ORF showed Mr Kurz’s Austrian People’s Party is projected to get 37.2% of the vote, a gain of 5.7 percentage points compared with 2017.
The Freedom Party was forecast to lose 10 points to get 16%, a sign that voters were punishing the party for over the video.
The centre-left Social Democrats were projected to lose 4.9 points and poll 22%, the party’s worst result since the Second World War.
The Alpine country of 8.8 million has been run by a non-partisan interim administration since June, after the video was released.
About 6.4 million Austrians aged 16 and older were eligible to vote, with pre-election polls forecasting a strong victory for Mr Kurz.
The 33-year-old will have to choose whether his conservative People’s Party will form a fresh coalition with a chastened Freedom Party or team up with the Social Democrats. Both were running neck-and-neck ahead of the vote.
“To go back to the Freedom Party, in the current situation this would be very difficult,” said Peter Hajek, a political analyst, but “the chemistry with the Social Democrats just doesn’t work”.
The Social Democrats, who have led many of post-war Austria’s governing coalitions, have failed to capitalise on the government’s collapse under leader Pamela Rendi-Wagner.
Mr Hajek said other options could see Mr Kurz team up with the Greens, who were forecast to get 14.3% of the vote, and the pro-business Neos, who were expected to get 7.4%. A coalition with just the Greens would also be possible.
The People’s Party won the 2017 election with 31.5% of the vote, with the Social Democrats taking 26.9% and the Freedom Party 26%.