An estimated six million people are eligible to vote, electing not just a president but also members of Congress, mayors and members of the Central American parliament.
"We hope this will be a civic celebration," said David Matamoros, head of the Supreme Electoral Tribunal, in declaring the polls open.
Hernandez's conservative National Party -- which controls the executive, legislative and judicial branches of government -- contends that a 2015 Supreme Court ruling allows his re- election.
Hernandez cast his vote early in his hometown of Gracias, in mountainous western Honduras, accompanied by his daughter and several National Party deputies.
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"Four more years," supporters chanted as he arrived. Hernandez told reporters he had been up early, messaging with organisers to be sure the elections would take place smoothly.
This small country, in the heart of the "Northern Triangle" of Central America where gangs and poverty reign, has one of the highest murder rates in the world, though that metric has fallen under Hernandez's four years in office.
That year, then-president Manuel Zelaya was deposed by the armed forces, with backing from the right and from powerful businessmen, for nudging closer to Venezuela's Hugo Chavez.
Zelaya was notably accused of wanting to change the constitution to vie for a second term.
Hernandez, 49, who came to power in 2013, was seen as the frontrunner going into today's election, out of a field of nine candidates.
His closest rivals are Salvador Nasralla, a 64-year-old TV anchor-turned-politician who represents the leftwing Opposition Alliance Against the Dictatorship coalition, and Luis Zelaya (not related to Manuel Zelaya), 50, who is the candidate of the right-leaning Liberal Party.
But some analysts warned the calm was deceptive, and tensions could boil over because of the president's desire to hold on to power.
"For the first time, it's not a race between conservatives and liberals, but between a dictatorship and democracy," said Victor Meza, a political analyst at the Honduras Documentation Center.
Alexander Main, an analyst at the US-based Centre for Economic and Policy Research, questioned Honduras' law-and- order achievements in an opinion piece written for The Hill, an online political news outlet.
Hernandez's top rivals in the race accuse the electoral board of preparing poll fraud to declare the incumbent president the victor. The Supreme Electoral Tribunal denies that.
"I hope you won't get discouraged when false information starts going around. We need to stay vigilant," Nasralla told his supporters on Friday.
One of the judges on the electoral tribunal, Marco Ramiro Lobo, told AFP that "our obligation is to guarantee a transparent electoral process which has verification mechanisms."
But Marvin Barahona, a political science researcher, said the elections posed the risk of a "new crisis" because of the Supreme Court decision opening the way for Hernandez's bid.
Apart from the presidential election, Sunday balloting will also decide the country's three vice presidency posts, the 128-seat congress, 20 representatives in the Central American Parliament, and the mayors of 298 municipalities.