Polling stations opened at 6am (04:00 GMT) on Sunday and are set to close at 8pm.
Saturday's opinion polls put Tusk on course for a victory with the support of about 43 per cent of the electorate.
The parliamentary election was called two years early after the collapse of the prime minister's last coalition in a row over a corruption investigation.
Many Poles support the twins' Law and Justice (PiS) party, backing its social policy and its uncompromising defence of what it says are Poland's interests in talks with the European Union.
Opponents see them as stubborn eurosceptics, obsessed with investigating ex-communists and corruption, who have done little to aid Poland's flourishing economy.
|Barnaby Phillips reports from Warsaw|
In his campaign manifesto, Tusk also said one of his top 10 priorities would be withdrawing Poland's 900 troops from Iraq, a pledge that could prove popular.
He has also vowed to patch up strained relations with Poland's EU partners.
But Jaroslaw Kaczynski's conservative message goes down well in rural Poland, although in the country's larger cities many people worry that he is dividing society.
The twins have won support among Catholics in what is a conservative religious country.
One PiS supporter, Tomasz Zbrug, told Al Jazeera after weekly mass: "Finally, Poland has something to say to the rest of the European Union.
"It has an international profile. It is developing into a strong country at home, but also abroad."
Dariusz Dolczewski, a member of Tusk's Civic Platform (PO) party, says he wants a country that is open to Europe.
He told Al Jazeera: "They don't have the capability to have the rule of government, to rule Poland. Poland needs freedom.
"Poland needs investors that will come, that will need freedom, but PiS doesn't work effectively they're just incapable of such things."
Pawel Szydlowski, a 27-year-old financial analyst who plans to vote for Tusk's Civic Platform, said: "If Law and Justice wins, it means we will move backward to the nationalist and xenophobic attitudes of early 20th century."
"We will never get any compensation from Germany" for the second world war, he said,"but we can do business with them. We have to look to the future."
The PO, if successful at the polls, could rule with the Polish Peasant's party (PSL), with which it already runs several local authorities.
The liberals may also be forced to turn to the Left and Democrats (LiD), an alliance steered by ex-communists, despite the reticence of some in PO's conservative wing.
Kaczynski's former allies from the far-right League of Polish Families (LPR) and the populist Self-Defence (Samoobrona) movement are expected to lose their seats.
PiS could try to work with the conservative wing of PO, but analysts say the bitterness of the past two years makes that unlikely.
Lech Kaczynski, the president, will still be in power whatever Sunday's result, since his five-year presidential term runs until 2010.
More than 30 million Poles over the age of 18 are eligible to vote.
They will elect 460 members of the lower house (Sejm) and 100 senators for four-year terms.
To win seats, political parties must gain at least five per cent of the nationwide popular vote.
Seats are distributed according to the percentage of the vote a party wins, but bigger parties or groups are given a higher proportion.
Senators are chosen by constituency according to a first-past-the-post electoral system, normally benefiting bigger parties.
Parliament must convene within 30 days of the election. The president must name a candidate for prime minister within 14 days of that.