But in Iran, even landslides at the ballot box do not equate to policymaking influence. All key decisions - including nuclear efforts, defense, and foreign affairs - remain solidly in the hands of the ruling clerics and their powerful protectors, the Revolutionary Guard.
What Rowhani's victory does is reopen space for moderate and liberal voices that have been largely muzzled in reprisal for massive protests and clashes in 2009 over claims the vote was rigged to deny reformists the presidency.
Rowhani's supporters also viewed the election as a rebuke of uncompromising policies that have left the Islamic Republic increasingly isolated and under biting sanctions from the West over Tehran's nuclear program. Rowhani, 64, is hardly a radical - having served in governments and in the highly sensitive role of nuclear negotiator - but he has taken a strong stance against the combative international policies of outgoing President Mahmoud Ahmadinejad and others.
"I thank God that once again rationality and moderation has shined on Iran," Rowhani said on state TV after results were announced. "This is the victory of wisdom, a victory of moderation, and a victory of commitment over extremism."
His emphasis on outreach could sharply lower the political temperature between Iran and the West - including Israel - and perhaps nudge the ruling establishment toward more flexible approaches in possible renewed nuclear talks with the U.S. and world powers. Rowhani also has added leverage with his political godfather and ally, former President Akbar Hashemi Rafsanjani, who was blocked from the ballot but now can exert influence from the wings.
Alireza Nader, a senior policy analyst at the Rand Corp. who follows Iranian affairs, described Rowhani as a de facto hero for reformists who couldn't support any of the other five candidates on the ballot.
"It remains to be seen how much room will be given to Rowhani by Supreme Leader Ayatollah Ali Khamenei and the Revolutionary Guard," he cautioned.
Just a week ago, Rowhani - the only cleric in the race - seemed greatly overshadowed by candidates with much deeper ties to the ruling theocracy and Revolutionary Guard, including hard-line nuclear negotiator Saeed Jalili and Tehran Mayor Mohammad Bagher Qalibaf.
But Rowhani gained momentum: first with endorsements from Rafsanjani and another moderate-minded former president Mohammad Khatami. Then artists, activist and opposition leaders joined. In the span of a few days, Rowhani was drawing huge crowds and the race - once seen as firmly in the control of the ruling system - was suddenly transformed.
In the end, Rowhani narrowly cleared the margin that would have forced a two-candidate runoff. The Interior Ministry said Rowhani took 50.7 percent of the more than 36 million votes cast, well ahead of Qalibaf with about 16.5 percent. Jalili came in third with 11.3 percent, followed by conservative Mohsen Rezaei with 10.6 percent.
The White House congratulated Iranian voters for "their courage in making their voices heard" despite clampdowns that included severe restrictions on the Internet, a key tool of Iran's opposition. Washington urged Tehran's leadership to "heed the will of the Iranian people and make responsible choices," while noting the U.S. remained open for direct dialogue with Iran.