The results make a unilateral declaration of independence by Kosovo more likely, sparking concerns in the European Union about the ramifications of such a move.
With results from 90 percent of polling stations counted, independent election monitors say Thaci's PDK came in first with 34 percent of the vote.
The long-standing governing party, the Democratic League of Kosovo (LDK) founded by the late pro-independence icon Ibrahim Rugova, came in second with 22 percent -- a sharp drop from the 45 percent the party won in the 2004 elections.
Thaci, the former political leader of the Kosovo Liberation Army (UCK), is now widely expected to become prime minister. Current Prime Minister Agim Ceku, a former UCK commander who does not have a party of his own, is stepping down.
Speaking to cheering supporters in the capital Pristina, Thaci said the PDK's victory marks the beginning of a "new century" for the province, which is officially part of Serbia but has been run as a UN protectorate since 1999. The vote, said Thaci, "showed that Kosovo is ready to move forward toward freedom and independence."
Likewise, PDK Vice President Hajredin Kuqi said the party has "worked intensively for change" and is ready to lead the province.
Vehbi Miftari, a spokesman for the second-place finisher, the LDK, says his party recognizes "the validity of these elections" and will respect the results.
Despite the PDK's win, it will not be able to form a government on its own.
In an interview with RFE/RL's South Slavic and Albanian Languages Service, political analyst Baton Haxhiu said a coalition with the LDK is likely.
"I think that despite their competitive relations in the past, the PDK and LDK will form a coalition," Haxhiu said. "There will not be a government without an agreement between the two biggest political parties."
According to Haxhiu, a coalition agreement would depend on reaching agreement on key government posts like the foreign affairs and defense portfolios, the presidency -- which is currently held by the LDK's Fatmir Sejdiu -- and on Pristina's local government.
"If in these three elements an agreement is reached, then the rest will be easily achievable," Haxhiu said.
Despite internal differences between Kosovo's ethnic Albanian parties, they are all united in their drive for independence -- and the sooner, the better.
Thaci says parliament will declare independence from Serbia "immediately after December 10," the date when mediators from the United States, the European Union, and Russia are due to issue a report on efforts to reach a compromise between Serbia and Kosovo's 90-percent ethnic Albanian majority.
Officials say there is no hint of a deal being reached. Belgrade has offered broad autonomy within Serbia, but Kosovo's leaders say they will settle for nothing less than full independence.
European Union foreign ministers today urged Kosovo not to rush toward independence. The United States backs independence for Kosovo, but the EU is divided on the issue.
Germany, Spain, Slovakia, and Romania have been hesitant to back a unilateral declaration of independence.
EU ministers meeting in Brussels said today such a declaration could prompt Kosovo's Serbian minority to secede and the Serbian half of Bosnia-Herzegovina to proclaim statehood as well, sparking massive destabilization in the Balkans.
"Kosovo should be independent, but it shouldn't be an unmanaged, unilateral declaration," Jim Murphy, Britain's European affairs minister, said today. He also urged the EU not to allow Russia to block statehood, as it has done in the past.
Likewise, Swedish Foreign Minister Carl Bildt said he believes Thaci understands "that there is a difference between [being] a politician in opposition and being a responsible prime minister" and will act accordingly.
"Kosovo is already de facto independent from Serbia," Bildt said today. "I don't think Kosovo wants to be independent from the international community -- they want to be defended, protected by NATO, they want to be supported in every other way by the European Union."
Wolfgang Ischinger, a German diplomat who is heading negotiations between Belgrade and Pristina, is due to meet Serbian and Kosovo Albanian officials in Brussels on November 20.
The Kosovo Model
Kosovo's status issue has a broader impact beyond the Balkans. Many separatist regions -- including the post-Soviet frozen conflicts of Abkhazia, South Ossetia, and Transdniester -- are looking to Kosovo as a model for how their own issues may be resolved.
Kosovo's elections were marred by low turnout, as only 45 percent of the 1.5 million eligible voters cast ballots.
Kosovo's Serbian minority boycotted the election to protest the independence plans. Many ethnic Albanian voters -- weary of politicians' inability to address widespread poverty and corruption -- chose to skip the vote as well. Unemployment in the province is estimated at 60 percent.
Political analyst Blendi Fevziu told RFE/RL's South Slavic and Albanian Languages Service that Kosovar Albanians are deeply disappointed in their leaders.
"The low turnout of the voters is undoubtedly connected with a huge disappointment with political elite in Kosovo," Fevziu said. "This disappointment has come not only because the status issue -- which in the end is not in the hands of the Kosovars -- has been prolonged so much. It also comes from a very difficult economic situation and poor management in general."
Council of Europe observers called the turnout "alarmingly low" adding that it revealed "a profound dissatisfaction among the population."