Rouhani has spent four years trying to pull Iran out of its global isolation, reaching a 2015 deal with world powers that ended some sanctions in exchange for curbs to its nuclear programme.
But with US President Donald Trump threatening to scrap the deal, and visiting Iran's bitter regional rival Saudi Arabia this weekend, that policy of detente looks increasingly in jeopardy.
Raisi has agreed to stick by the nuclear accord but says Rouhani put too much trust in the West.
The election essentially became a two-horse race after two other candidates, conservative Tehran mayor Mohammad Bagher Ghalibaf and reformist Eshaq Jahangiri, dropped out this week to boost Raisi and Rouhani respectively.
Rouhani, a 68-year-old cleric, has tried to frame the election as a choice between greater civil liberties and "extremism", and unofficial polls still put him ahead.
But he has faced a much tougher campaign than anyone expected just a couple of months ago, as hardliners have savaged his economic record, saying his diplomatic efforts have done little to tackle poverty and unemployment.
A close ally and former pupil of supreme leader Ayatollah Ali Khamenei, he is seen as the preferred choice of the powerful security establishment, advocating a more self- sufficient "resistance economy" rather than a reliance on foreigners.
Raisi has tried to pick up working-class votes by promising more financial support, as well as playing on his status as a "seyed", or direct descendant of Prophet Mohammed.
"At the halfway point, we don't turn back," he tells voters.
He has vowed to work towards removing the remaining, non-nuclear sanctions imposed by the US, which have strangled Iran's efforts to sign trade deals with European and Asian countries.
That would be a tall order, given that Trump has launched a 90-day review to see whether he will stick by the nuclear deal at all, let alone remove any other sanctions.
While Iranians largely welcomed the reduced tensions with the West, the ongoing economic slump has taken a toll on morale.
Unemployment is officially stuck at 12.5 per cent -- close to 30 per cent for the young -- and many more are under-employed or struggling to get by.
Rouhani says he inherited a financial mess from his populist predecessor Mahmoud Ahmadinejad, who was dramatically barred from standing this year by the Guardian Council after falling foul of the conservative establishment.
That has left a vacuum for many working-class voters who fondly recall the construction boom, cash hand-outs and earthy rhetoric of Ahmadinejad's rule.
Supreme leader Ayatollah Ali Khamenei said a massive turnout was needed to show the continued popularity of the Islamic regime.
"Faced with the enemy, the people should show their determination and calm," he said today.
Despite the slump, many voters, particularly wealthier urbanites, are attracted to Rouhani's promise of greater social freedoms.
At his last major rally in Tehran, thousands chanted for reformist leaders locked up after mass protests in 2009.
Rouhani has made thinly veiled references to Raisi's past as a prosecutor during a period in the 1980s when many dissidents were executed.
"We've entered this election to tell those practising violence and extremism that your era is over.
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