According to the Central Electoral Commission some 33.73 percent of the 20 million plus electorate cast votes in the first five hours of the vote.
According to the Central Electoral Commission some 33.73 percent of the 20 million plus electorate cast votes in the first five hours of the vote -- exceeding the minimum turnout of a third of voters required to make the polls valid.
Voting at over 9,300 polling stations throughout the Muslim-majority Central Asian country with no tradition of competitive elections began at 0100 GMT and was due to close at 1500 GMT.
Mirziyoyev, who was appointed prime minister in 2003, became interim president following Karimov's death aged 78 in September from a stroke.
He cast his vote in the capital Tashkent before 0600 GMT according to state media.
Representing the same Liberal-Democratic Party that Karimov stood for in the last presidential vote in 2015, he is facing three other challengers in a bid to secure a five-year term.
But analysts noted that the other candidates are not critical of Mirziyoyev or the regime in the country bordering Afghanistan where Beijing, Moscow, and Washington all vie for influence.
"The format for Uzbek elections has not changed since Karimov's death because the regime has not had time to think of anything different," said Kamoliddin Rabbimov, an Uzbek political analyst who lives in France.
"If anything, efforts have been made to ensure other candidates are even more obscure because Mirziyoyev's stature among the population is not yet what Karimov's was," he told AFP.
"Uzbekistan has its own specific take on democracy. There will be no surprises here, unlike in America with Trump," he added.
Karimov's 27-year reign began in 1989 at the tail-end of the Soviet era, and was often criticised for extreme abuses of human rights.
Few expect 59-year-old Mirziyoyev to make serious political changes if elected after serving at the top of his predecessor's repressive state for so long.
But since coming to power Mirziyoyev has offered clemency to at least one prominent political prisoner while indicating his government will prioritise reforms to the heavily regulated state economy.
"Based on what he's done so far, I'd say he's trying to smooth the rough edges of Karimov's system," said Scott Radnitz, a regional expert at the University of Washington.
That system is prefaced on "tight political control and crony economics," Radnitz told AFP by email.
"It worked to retain the power structures and a low if steady level of growth, but it stifles ordinary people," he said.
As premier for 13 years Mirziyoyev was regularly touted as a potential successor to Karimov, along with current deputy prime minister Rustam Azimov and Karimov's eldest daughter Gulnara Karimova.
But businesswoman-cum-popstar Karimova, 44, has been reportedly under house arrest in the country since 2014 after publicly feuding with her mother and her younger sister Lola.
Neither Karimova nor her two children attended the strongman's September 3 funeral and her eldest son Islam Karimov jr., who lives in London, called on authorities to prove she was alive and well in a recent interview with the BBC.
With her situation at home unclear, Karimova is also the subject of a multi-year corruption probe targeting Western telecoms firms that US and European investigators say paid her billions of dollars in bribes to secure access to the national market.
Under Karimov, Uzbekistan enjoyed mostly cordial relations with foreign powers active in the region but kept all of them at arm's length while regularly threatening smaller neighbours Kyrgyzstan and Tajikistan.
The country with the region's largest army exited a Moscow-led security bloc in 2012.
In 2005, it ejected US forces from a military base used for Afghanistan operations over Washington's human rights criticisms.
Mirziyoyev was quick to meet with Russian leader Vladimir Putin after Karimov's death and last month hosted President Recep Tayyip Erdogan of Turkey, with whom Karimov enjoyed patchy relations.
"Under Karimov, Uzbekistan withdrew into itself, to its great cost, and this may be the main difference under Mirziyoyev," said analyst Rabbimov.
"The policy of not joining military blocs and hosting bases may remain, but I think Uzbekistan will begin to participate in more international initiatives. He will see the country can't survive in isolation."