Following a low-key campaign in the European Union's most easterly member, polls put the conservative in the lead as he claims credit for an economic recovery from a debilitating crisis in 2013.
But Anastasiades, 71, looks unlikely to win a first round outright.
He is expected to face a February 4 run-off against either communist-backed Stavros Malas or Nikolas Papadopoulos, a former president's son who takes a tougher line on peace efforts.
Apathy among the roughly 550,000 registered voters appears high and opponents have failed to land a major blow on the former lawyer as he seeks a second five-year term.
There is set to be intense horse-trading if the first round is not decisive and a backroom deal could still thwart Anastasiades.
"But we need to see what alliances are formed for a second round."
As always, the nearly 44-year division of the island between the internationally recognised Greek-majority Republic of Cyprus and a Turkish Cypriot statelet in the north looms large.
In July, two years of UN-backed talks between Anastasiades and Turkish Cypriot leader Mustafa Akinci came closer than ever to reunifying the island but collapsed in acrimony before a deal.
Despite the failure to bridge key issues, including the future of tens of thousands of Turkish troops in the north, Anastasiades insists he wants talks with Akinci to restart soon.
But there is deep scepticism over whether there is the political will to make a breakthrough.
At the only televised debate before the vote, opponents laid into Anastasiades for being either too pliant or not determined enough to reach a deal last year.
Signs are that the road to reunification will only get tougher as fatigue mounts after decades of failure.
In the north, parliamentary elections this month saw parties opposed to reunification perform strongly.
While the "national problem" is ever present, this time around the economy has been a dominant issue.
When Anastasiades took over, the banking sector was in meltdown and he took a 10-billion-euro (more than USD 12- billion) bailout that entailed biting austerity measures.
That included a drastic haircut on accounts of over 100,000 euros held in the country's biggest lender, Bank of Cyprus.
Since then the economy has rebounded faster than many expected and growth has been steady since 2015.
Tourism reached a record high last year and explorations are going on for oil and gas offshore.
But the economy is still smaller than it was before the crisis, unemployment is around 11 per cent and banks are awash with bad loans.
"The recovery is relative," Mullen said.
Polls open at 0500 GMT and close at 1600 GMT with final results expected late today.