Partial results show the HDZ party is to win about 60 seats, with more than 50 for the ruling alliance led by the Social Democrats.
The conservatives are now expected to enter talks to form a coalition.
The migration crisis was one of the main issues. More than 320,000 migrants have passed through Croatia this year.
"The victory brought us responsibility to lead our country, which is in a difficult situation," HDZ leader Tomislav Karamarko told supporters.
"Whoever wants to fight with us for the quality of life in Croatia is welcome."
The big winner looks to be the third force in the election - an alliance of independent candidates known as Most (Bridge), which is expected to claim about 19 seats.
Croatia election: Opposition conservatives claim victory
09 November 2015
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Croatia`s opposition conservatives have declared victory in parliamentary elections, but face a challenge to form a government.
