The communists, in power since 2001, were credited on Sunday with around 42% of the vote and the centrist opposition Bloc for Democratic Moldova (BDM) about 28%, according to the exit poll by the the Public Politics Institute.
The nationalist Popular Christian Democratic Party (PPCD) was running in third place with about 14% of the vote, according to the survey of some 13,000 voters at 220 polling stations across the country.
Voter turnout was estimated at nearly 59% of Moldova's 2.3 million voters.
Although the communists came to power on a pro-Russian ticket, they have since done an about-face, partly because of disagreements with Moscow over its troop presence in the separatist region of Trandsdniestr, which Russia has tacitly supported since it broke away from Moldova after a short war in 1992.
The communists and their main competitors - both the centrist BDM and nationalist PPCD - all declare themselves to be pro-Western, offering voters a choice between various degrees of integration.
Exit poll: Communists 42%, BDM
28%, PCDP 14% of the votes
Tensions with Moscow have risen in recent weeks, with Moldovan authorities denying entry to Russian electoral observers and expelling others.
President Vladimir Voronin has also accused Russia of interference.
Anti Russian axis
Before the poll Voronin held meetings with the leaders of Ukraine and Georgia, arousing Russian suspicions about the possible formation of an anti-Russian axis of the three pro-Western former Soviet republics.
Russia has fumed at the change in its former satellite - which was historically part of Romania, but became a Soviet constituent republic - accusing Moldova of deliberately seeking confrontation.
With a population of 4.5 million people, Moldova is one of the poorest of the former Soviet states and considered to be Europe's poorest country, with a per capita gross national product of barely $600.