The National Electoral Commission will wait for votes from abroad until September 29, before publishing the official results.
The conservative-led government has frequently been accused of corruption.
The opposition left are showing unity in a bid to regain power after four years of centre-right rule.
Jansa and his SDS party are claiming credit for the country's increased prosperity.
But recent surveys show Borut Pahor's opposition centre-left Social Democrats (SD) and their allies, who offer a stronger welfare state for the country's two million people, could win more seats as a unified faction in parliament than the SDS and its partners.
The new government's priority will be to cut overall spending and curb high inflation while keeping the booming economy on track despite a global financial slowdown.
Analysts expect a high degree of political continuity regardless of the outcome, but caution that either party will need partners in the new government and coalition talks could last for weeks or months.
"Things have to change. People in Slovenia can no longer live like this," Matjaz Gabrijelcic, a car salesman, said.
"Inflation is sky high and the average wages are barely enough for people to live on. We need a government whose preoccupation are the little people."
Slovenia joined the European Union in 2004, became a Nato member and was also the first east European state to adopt the Euro in January 2007.
While its economy thrived due to rising exports, inflation rose steadily to reach a six-year high of 6.9 per cent - the highest in the Eurozone.
Unemployment in the country is at six per cent, the highest among the 15 countries which use the Euro currency.