The government of the southern Russian republic had resigned after lawmakers on February 20 backed Mukhu Aliyev as the republic's new president.
Minutes after the March 6 vote, Aliyev signed a decree appointing Zainalov to the post.
Zainalov was previously Daghestan's representative in Russia's Federation Council, the upper chamber of the national parliament.
Daghestani lawmakers also elected the republic's former prime minister, Atay Aliyev, as Daghestan's new representative in the Federation Council.
RFE/RL Russia Report
SUBSCRIBE For news and analysis on Russia by e-mail, subscribe to "RFE/RL Russia Report."