Liberal reformer Mesic on Sunday captured 49.03% of votes while his main rival, Jadranka Kosor of the ruling conservative Croatian Democratic Union (HDZ), trailed behind with 20.18%.
Mesic needed to get more than 50% for another term without going through a second round run-off.
Mesic and Kosor, both supporting Croatia's efforts to join the European Union in this decade, will contest a run-off on 16 January.
A jubilant Mesic urged voters to turn out in big numbers for the run-off - following a low turnout of 51% on Sunday.
"Croatia must be a modern, European and democratic country with satisfied citizens. It will be possible only if we change many things," he said after results were announced.
A woman president
Kosor said Croatia was ready for a woman president. "I am very happy that for the first time we have two candidates of which one is a woman," she said, adding that it "shows the maturity of voters".
The 70-year-old Mesic was heavily favoured to win the vote to lead the former war-torn Yugoslav republic, with exit polls released immediately after voting stations closed showing he might win the 50% needed to avoid the run-off.
"Croatia must be a modern, European and democratic country with satisfied citizens. It will be possible only if we change many things"
President Stjepan Mesic
Wealthy Croatian-US businessman Boris Miksic finished third with 17.8% of the vote, the electoral commission said.
The strong showing of Miksic, an outsider on Croatia's political
scene, whose support was not expected to go beyond single digits, was described as a protest vote.
Exit polls had put Miksic ahead of Kosor, in what would have
been a major humiliation for her ruling HDZ.
During a lacklustre campaign, Mesic and Kosor both pledged a
better future for Croatians along the same lines - EU membership, the strengthening of the rule of law and fighting corruption.
Croatia has been put on a fast track to European integration
Only about half of the 4.4 million
eligible voters cast their ballots
with Brussels deciding last month to kick off membership talks in March.
It hopes to fulfil the membership criteria by 2007 but its bid
depends on full cooperation with the UN war crimes court following the Balkans wars of the 1990s which will be closely monitored by Brussels.
Joining the EU and the handover of suspects of genocide have been two predominant issues in the presidential campaign.
Although Mesic favours cooperating with the tribunal at The Hague, he insists Croats charged with war crimes must face justice at home.
Mesic's candidacy is supported by the three main centre-left
opposition parties who were defeated by the HDZ in legislative polls in November 2003.