Hundreds of people clapped and cheered as a giant screen outside her National League for Democracy (NLD) party headquarters in Yangon announced the Nobel Peace Prize winner had won a parliamentary seat for the first time.
Some people wept with joy at the news, which if confirmed would mark a stunning turnaround for the former political prisoner, who was locked up by the former junta for most of the past 22 years.
"We have been waiting for this day for a long time. I'm so happy," said NLD supporter Kalyar, who goes by one name.
Suu Kyi won an estimated 99 percent of the votes in Kawhmu constituency, according to NLD official Soe Win, based on the party's own tally. There was no independent confirmation and official results were expected within a week.
The party also claimed it was on course to win all 44 seats it contested in the by-elections, in which a total of 45 seats were at stake -- not enough to threaten the army-backed ruling party's huge majority.
Observers believe Myanmar's new reform-minded quasi-civilian government wanted Suu Kyi to win a place in parliament to burnish its reform credentials and smooth the way for an easing of Western sanctions.
Many of her supporters had earlier waited for hours in searing heat to catch a glimpse of the 66-year-old Suu Kyi, who was running for political office for the first time.
Her main rival in the rural Kawhmu constituency, two hours' drive from Yangon, was a former military doctor with the ruling Union Solidarity and Development Party.
Voters, some in traditional ethnic Karen dress, queued patiently to cast their votes. In stark contrast to life under the junta, many openly expressed their support and affection for "The Lady".
"There's only been one person for us for 20 years," said Tin Zaw Win.
"We believe in her and want to vote for her. Almost my whole village will vote for Aunt Suu," he added.
Some people complained that their names were missing from the voter lists, although it was unclear how many were affected.
"I want to vote for Mother Suu but they haven't given me my ballot paper so I'm here to demand it," Zin Min Soe told AFP at a polling station.
"They can't just lose my vote," he said.
The polls were also marred somewhat by allegations of ballot-paper irregularities, notably that wax had been put over the check box for the NLD that could be rubbed off later to cancel the vote.
It was not immediately clear how widespread irregularities were.
"This is happening around the country," NLD spokesman Nyan Win told AFP. "I have sent a complaint letter to the union election commission."
In the run-up to the eagerly awaited vote, the party decried alleged intimidation of candidates and other irregularities.
Suu Kyi said on Friday that the poll could not be considered "a genuinely free and fair election" but stopped short of announcing a boycott.
A 2010 general election, won by the military's political proxies, was plagued by complaints of cheating and the exclusion of Suu Kyi, who was released from seven straight years of house arrest shortly afterwards.
The seats being contested Sunday were made vacant by MPs who joined the government.
The NLD swept to a landslide election victory in 1990, but the generals who ruled the country formerly known as Burma for decades until last year never recognised the result.
A gruelling schedule of rallies and speeches took its toll on the opposition leader, who cancelled campaigning in the week before the vote after she fell ill.
Suu Kyi appeared to have recovered her strength by election day, smiling broadly when she emerged just after dawn from the village house where she was staying in Kawhmu.
After almost half a century of military rule, the junta in March last year handed power to a new government led by President Thein Sein, one of a clutch of former generals who shed their uniforms to contest the 2010 election.
Since then, the regime has surprised even its critics with a string of reforms such as releasing hundreds of political prisoners.
But remaining political detainees, fighting between government troops and ethnic rebels, and alleged human rights abuses remain major concerns for Western nations which have imposed sanctions on the regime.
Unlike in 2010, the government allowed foreign observers and journalists to witness Sunday's polls. More than six million people were eligible to vote.