Opinion polls taken before the election had predicted a similar result.
Those surveys also showed that Komorowski would easily beat Kaczynski in a second round.
Victory would be a boon for Komorowski's Civic Platform party, unlocking a political logjam more than a year before the autumn 2011 parliamentary elections.
The election date was moved up after Lech Kaczynski was killed in a plane crash along with his wife and 94 others near the western Russian town of Smolensk on April 10.
Nazanine Moshiri, Al Jazeera's correspondent in Warsaw, said that there was a lot of sympathy for Kaczynski, following the death of his twin brother and as his mother is seriously ill in hospital.
"But there are other things at stake in this election, like the direction Poland is heading. Lech was very much against Poland joining the Euro and withdrawing troops from Afghanistan.
"He vetoed a lot of policies the government was trying to bring in to modernise and liberalise the market. So there's a lot of things on people's minds here."
Moshiri said that Komorowski is pro-Euope and pro-reforms, going against Jaroslaw Kaczynski's support base.
"So this really is a contest between two different visions of what the future should be here in Poland," Moshiri said.