PM Victor Ponta led in the first round with 40% to 30% for Klaus Iohannis, an ethnic German mayor.
The social democrat has promised both to reduce the budget deficit and increase pensions and the minimum wage.
President Traian Basescu, Victor Ponta’s long-time political foe, cannot stand for re-election after serving two terms.
Since taking office as prime minister two years ago, Victor Ponta, 42, has overseen economic growth and political stability in Romania.
Klaus Iohannis, 55, has promised to crack down on wrongdoing and strengthen the independence of the judicial system.
However, critics accuse the mayor of Sibiu, a town of around 155,000 people in Transylvania, of seeking to avoid confrontation with the outspoken Victor Ponta, who has maintained his lead in opinion polls.
As prime minister, Victor Ponta often feuded with President Traian Basescu and their poor relations delayed much-needed reforms in the public sector.
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