MOSCOW—Uzbekistan’s acting President Shavkat Mirziyoyev won a resounding victory in the country’s first presidential election since the death of longtime authoritarian leader Islam Karimov.

The vote was carried out peacefully in Central Asia’s most populous country, which saw economic decline under the rule of Mr. Karimovdue to rampant corruption and international criticism over accusations of human rights abuses. Observers from the Organization for Security and Cooperation in Europe’s vote monitoring body said the election lacked competition.

Mr. Mirziyoyev worked as prime minister under Mr. Karimov since 2003 until the leader’s death in late September of this year, when he quickly circumvented the constitution to take over as acting president. Uzbekistan’s central election committee said preliminary results showed Mr. Mirziyoyev had won almost 89 % of the vote and a nearly 88% vote turnout.

Mr. Mirziyoyev, who represented the Liberal Democratic Party of Uzbekistan in the election, one of four sanctioned parties in the country, has praised the rule of his predecessor, whose rule was considered by analysts as one of the most repressive in the world.

But Mr. Mirziyoyev, who also has a reported reputation for brutality, has suggested he would focus on the country’s moribund economy restrained for years by corruption and cumbersome bureaucracy, including foreign-exchange controls that have benefited various power groups within the government.

During his term as acting president, Mr. Mirziyoyev has already moved to improve relations with other central Asian countries that Mr. Karimov isolated during his 25-year rule.

He has also taken steps to liberalize the currency market, and a presidential order open to revisions until Dec. 14 is aimed at cutting cumbersome regulations that have hindered economic growth. Those laws, together with a lack of independent courts and rampant graft, have scared off foreign investors and quashed economic growth.

“It remains too early to tell whether the reform pledges are purely token populist gestures and campaign rhetoric or whether they will result in something more substantive,” said Kate Mallinson,independent Central Asia analyst.

Running against Mr. Mirziyoyev were representatives from Uzbekistan’s three other parties: Sarvar Otamuradov, of Uzbekistan National Revival Democratic Party; Narimon Umarov, of the Justice Social Democratic Party and Khatamjon Ketmonov of the People’s Democratic Party of Uzbekistan.

Uzbekistan’s foreign policy may see a meaningful shift, as analysts say he has a better relationship with Russian President Vladimir Putin than his predecessor did. Mr. Putin sent a congratulatory note less than 20 minutes following the announcement of Mr. Mirziyoyev’s win, Interfax reported.

Mr. Karimov, Uzbekistan’s only president since the fall of the Soviet Union, strengthened ties with the U.S. following the Sept. 11 terrorist attacks. He allowed a U.S.-led coalition to use an air base on Uzbek territory for bombing sorties on Taliban targets in neighboring Afghanistan.

Several years later, however, he kicked coalition members out of the base amid fears of a color revolution like those that unseated other leaders in former-Soviet republics Georgia and Ukraine.

Write to Thomas Grove at thomas.grove@wsj.com