About 162,000 people were eligible to vote for the 50-seat parliament in the breakaway territory, the administration of which is only recognised by Turkey.
The election outcome would not directly affect Talat, who began unity talks with Greek Cypriots in September.
But victory for the UBP is likely to limit Talat's ability to negotiate a settlement.
Cyprus has been divided since 1974 when Turkey invaded in response to a coup
by supporters of reunification with Greece.
The basis of the talks had been reuniting the island as a bizonal federation, though the UBP said it wanted a rethink of the process.
Talat has held talks with Dimitris Christofias, the Greek Cypriot president, which many have viewed as the most realistic attempts at a lasting peace in decades.
His Republican Turkish Party had 25 deputies in the last assembly, while the UBP had only 16.
Talat said that regardless of who won, the outcome should not be allowed to disrupt current peace negotiations.
"A government in [Northern Cyrpus] that seeks to scupper the talks will also be harming Turkey's EU accession process," he told Havadis, a Turkish Cypriot daily.
The UBP, led by Dervis Eroglu, had a 15 point lead over Talat's party. Eroglu said that a unified Cyprus should not be the only option and promised to appoint a representative to accompany Talat in negotiations with Christofias.
"Everything will be easier if it is universally accepted that we are a nation and that we have a state," Eroglu said.
Greek Cypriots represent Cyprus in the European Union, and say they will not allow Turkey to join the bloc as long as the island remains divided.