Opinion surveys conducted last week indicated that Duda could have a more difficult time in a runoff.
"There were nine other candidates fighting for [the presidency], DW's Wojciech Szymanski said. "There was a candidate of the leftist party, for example, so [...] who will the voters of a leftist party support in the second round?"
"It is, of course, more possible that they would vote for Mr Trzaskowski than Mr Duda — a candidate of a right-wing national conservative party."
Polls based on actual results were expected to be released around midnight and 3 a.m. Poland's state electoral commission said it would release the final official results by Wednesday evening.
Clash of values
Duda campaigned on a conservative social agenda, and a pledge to safeguard traditional family values in the predominantly Catholic country.
He backed anti-abortion legislation and echoed PiS attacks on LGBT rights and liberal values.
"I believe that the Law and Justice Party […] knows that scaremongering is always a powerful weapon in a campaign in Poland, so they used this to mobilize its very hard-core electorate," said DW's Wojciech Szymanski.
Trzaskowski instead supported gay rights and said he is open to the idea of same-sex civil partnerships.
Campaigning with the slogan "Enough is Enough," Trzaskowski promised a different Poland, although many see his PO party as weak and ineffectual.
No candidate was expected to gain the level of 50% plus one vote, which they would need to secure the presidency in the first round.
Duda is expected to lead, but is likely to go head-to-head with Trzaskowski in a July 12 run-off, opinion polls show.
Homophobia on the rise
Since winning power in 2015, both Duda and the PiS have stoked tensions with the EU and provoked repeated street protests at home for controversial laws giving the party control over the top courts and other key judicial bodies.
While PiS insists the changes are needed to weed out judicial corruption, critics and the EU insist they erode judicial independence and democracy just three decades after Poland shed communism.