VILNIUS (Reuters) - Lithuanian president Dalia Grybauskaite won a second term in run-off elections on Sunday as her anti-Russian political message struck a chord among voters.

Grybauskaite, a 58-year-old former European Budget Commissioner and former minister of finance, attracted 57.9 percent of the votes in the nation of 3 million, the electoral commission said. Zigmantas Balcytis, a social democrat supported by prime minister Algirdas Butkevicius, received 40.1 percent.

The president holds considerable power in Lithuania, appointing government ministers, as well as judges, the head of the central bank and the Lithuanian member of the European Commission - though needing the approval of parliament or the prime minister for most appointments.

(Reporting by Andrius Sytas; Editing by John Stonestreet)