Her National League for Democracy (NLD) party announced to loud cheers at its headquarters that the Nobel Peace Prize laureate had won in Kawhmu, south-west of the commercial capital Yangon, raising the prospect of her first role in Government after a two-decade struggle against dictatorship.
Burma's Election Commission had yet to confirm any results from the by-elections for 45 legislative seats.
The United States and European Union have hinted some sanctions imposed over the past two decades in response to human rights abuses may be lifted if the election is free and fair, unleashing a wave of investment in the impoverished, resource-rich country.
The charismatic and wildly popular Ms Suu Kyi had complained last week of electoral irregularities, though none large enough to derail her party's bid for 44 seats. She made no immediate comment on her victory.
Voting was observed by delegates from the European Union and the Association of South East Asian Nations (ASEAN).
"Whatever irregularities we saw in the polling stations we visited did not seem to be out of bad will or intentions," said EU delegate Malgorzata Wasilewska. "It was more lack of experience."
She stressed, however, that the EU had only visited a small number of polling stations and that irregularities could still occur in the counting process.
While Ms Suu Kyi's party might end up with just a few parliamentary seats, many expect her to exert disproportionate influence.
Some Burmese wonder if conservatives will dare oppose her in Parliament given her popularity, especially ahead of a general election in 2015. Many MPs want to be seen to be aligned with her, basking in her popular support.
From dawn, voters quietly filed into polling stations, some gushing with excitement after casting ballots for Ms Suu Kyi, or "Aunty Suu" as she is affectionately known.
Among her supporters who voted early yesterday in the rustic constituency of bamboo-thatched homes in Kawhmu, there was little doubt she would win. "My whole family voted for her and I am sure all relatives and friends of us will vote for her too," said Naw Ohn Kyi, 59, a farmer.
To be regarded as credible, the vote needs the blessing of Ms Suu Kyi, who was freed from house arrest in November 2010, six days after a widely criticised general election that paved the way for the end of 49 years of direct army rule and the opening of a parliament stacked with retired and serving soldiers.
President Thein Sein, a general in the former military junta, instituted the biggest political reforms since the military took power in a 1962 coup.
The Government has freed hundreds of political prisoners, held peace talks with ethnic rebels, relaxed media censorship, allowed trade unions, and shown signs of pulling back from the orbit of its giant neighbour, China.
Hillary Clinton made the first visit to the country by a US secretary of state since 1955. Business executives, mostly from Asia but many from Europe, have swarmed to Yangon in recent weeks to hunt for investment opportunities.