The Warsaw Voice reported an exit poll quoted by Polish television broadcaster TVP gave the CP 39.6 percent to 30.1 percent for the Law and Justice party of former Primer Minister Jaroslaw Kaczynski.
It means Tusk's party could retain power for a second term in a coalition, a political first since Poland moved from communism to democracy in 1990.
Palikot Movement party finished third with 10.1 percent of the vote, followed by the Polish People's party with 8.2 percent and the Democratic Left Alliance at 7.7 percent.
Voter turnout was pegged at 47.7 percent, down about 6 percentage points from 2007.
"I believe the next four years are an even greater challenge," Tusk said in claiming victory.
"We will have to work twice as hard and act twice as fast. Poles have the right to an increasingly high quality of life."
Kaczynski lamented that "unfortunately, a large part of society decided that things are fine as they are." However, he said, "The day of victory will come. Poland needs changes and these changes will happen."
The opening of a polling station in Zielona Gora was delayed by more than 2 hours as police evacuated the area to examine a suspected explosive device, which turned out to be a hoax, Polsa Agenja Prasowa reported. A 70-year-old man was arrested in the false alarm.
In a separate incident, police were alerted to the possibility of a bomb at a polling station in Warsaw. Officials searched the area but found nothing after receiving a call from Britain. British authorities said the call was traced to a 40-year-old Pole who was under the influence of alcohol.