The run-off election will decide whether former foreign minister Abdullah Abdullah or ex-World Bank economist Ashraf Ghani leads the country into a new era with declining international military and civilian assistance.
President Hamid Karzai is due to step down after ruling the country since 2001, when a US-led offensive ousted the austere Taliban regime for sheltering Al-Qaeda militants behind the 9/11 attacks.
Afghan officials and international allies are hoping for a repeat of the first-round vote in April, when the insurgents failed to launch a single high-profile attack and voter turnout was more than 50 per cent.
But the stakes are high with the Taliban issuing specific threats to target polling stations and widespread fears that electoral fraud could produce a contested result.
In a sign of international concern, UN head of mission Jan Kubis issued a stark warning to candidates' supporters not to resort to the ballot-box stuffing that marred the 2009 election when Karzai retained power.
"Do not commit fraud. Do not use intimidation or manipulation to favour your candidate," Kubis said ahead of polling day, when voting stations opened on time at 7:00 am (0230 GMT).
Abdullah secured 45 per cent of the first-round vote, with Ghani on 31.6 per cent after investigations into multiple fraud claims for both sides.
The two candidates came top of an eight-man field, triggering the run-off election as neither reached the 50 per cent threshold needed for outright victory.
A smooth handover in Afghanistan's first democratic transfer of power would be a major achievement for the international effort to establish a functioning state after the depredations of the Taliban era.
Harsh terrain and poor roads make holding an Afghan election a logistical challenge, with thousands of donkeys used to transport ballot boxes to remote villages.
Counting the ballot will take weeks. The preliminary result is due on July 2 and a final result on July 22.
Ahead of the vote, the Taliban said that polling booths would be targeted by "non-stop" assaults.
"By holding elections, the Americans want to impose their stooges on the people," the insurgents said on their website.
More than seven million people voted on April 5, but turnout today may be lower after an apparent dip in public interest.