In a first round on January 28, conservative Anastasiades garnered 35.5 percent of the ballots, while communist-backed opponent Stavros Malas picked up 30 percent.
The head-to-head showdown Sunday is a rerun of the 2013 vote that saw Anastasiades cruise into office in the European Union’s most easterly member.
But, with last week’s losing candidates refusing to back either hopeful, this time around it looks set to be closer as the former lawyer seeks a second and final five-year term.
“Anastasiades still appears to have the advantage but there are many question marks with regards to how the voters will go,” analyst Christophoros Christophorou told AFP.
As always, the nearly 44-year division of the eastern Mediterranean island between the Greek-majority Republic of Cyprus and a Turkish-backed statelet looms large.
Anastasiades, 71, has pledged fresh talks with Turkish Cypriot leader Mustafa Akinci despite the acrimonious collapse last July of UN-backed negotiations that cames closer than ever to sealing a deal.
Dovish former health minister Malas, 50, is one of the loudest proponents for finally reunifying the island and has slammed his opponent for not doing enough to reach an agreement.
The first-round success of the candidates seen as most keen on a deal has sparked hope that progress can be made.
But there remain major obstacles, including over the future of some 40,000 Turkish troops in the north, and deep scepticism that Nicosia or a nationalist government in Ankara are willing to compromise.
“The wider political framework in which this president comes to power is not conducive for a settlement,” said University of Nicosia professor Hubert Faustmann.
– Economic battle –
This time around the economy has been a dominant issue for the roughly 550,000-strong Greek Cypriot electorate as the island recovers from a 2013 financial crisis.
Anastasiades has claimed credit for an impressive recovery since agreeing a harsh 10-billion euro (more than $12-billion) bailout just weeks after taking power.
But major challenges remain despite record tourist numbers.
The economy is still smaller than before 2013, employment remains around 11 percent and banks are awash with bad loans.
AKEL — the communist party backing Malas — was in charge ahead of the crisis and is widely held responsible for tanking the economy.
Anastasiades has seized on this and warned Friday of a “return to the dogmatic policies that led us to the brink of bankruptcy”.
After a lacklustre race, apathy appears high as no candidate has captured the imagination of voters — especially young Greek Cypriots.
There was a record low turnout of just over 71 percent in the first round.
Polls open at 0500 GMT and close at 1600 GMT. Results and the inauguration of the next president are expected Sunday evening.