"Everything's now at heaven's disposal," Moon told reporters at a polling station in the southeastern port city of Busan. "I have put forward every bit of my energy."
Park, a five-term lawmaker, voted in Seoul and said she would wait for the "people's choice with a humble mind," calling on voters to "open a new era" for their nation.
South Koreans express deepening worry about the economy and disgust over the alleged involvement of aides close to Lee in corruption scandals.
Many voters blame Lee's hardline views for encouraging North Korea to conduct nuclear and missile tests including a rocket launch by Pyongyang last week that outsiders call a cover for a banned long-range missile test. Some also say ragged North-South relations led to two attacks blamed on Pyongyang that killed 50 South Koreans in 2010.
"I skipped breakfast to vote. I've been waiting to vote for five years. I think it's time to change the government," said 37-year-old Kim Young-jin, who voted for Moon at a polling station inside an apartment complex.
At one polling station in Seoul, young and old voters alike stood in line, despite a bitter cold snap. Wednesday is a national holiday in South Korea. Electric stoves inside the polling station warmed the line of voters that stretched longer as the sun rose. Polls opened at 6 a.m. local time. Some voters blew on their freezing hands as they hurried into the polling station.
"I believe in Park," Choi Yong-ja, a 59-year-old housekeeper, said as she left a polling station at a Seoul school. "She has abundant political experience."
The effort to create distance with incumbent Lee has been more difficult for Park, whose popularity rests on a staunchly conservative, anti-North Korea base of mostly older voters.
Both candidates propose pulling back from Lee's insistence that engagement with North Korea be linked to so-far-nonexistent nuclear disarmament progress by Pyongyang. Park, however, insists on more conditions than Moon.
Moon is a former chief of staff to Lee's predecessor, late President Roh Moo-hyun, who championed the so-called "sunshine policy" of no-strings-attached aid for Pyongyang.
Moon wants an early summit with North Korean leader Kim Jong Un. Park has also held out the possibility of such a meeting, but only if it's "an honest dialogue on issues of mutual concern."
Whoever wins the presidential Blue House will set the initial tone for new North Korea policy not just in Seoul but in Washington, Beijing and Tokyo. All those governments have recently undergone an election, a change of leadership or both.
A Moon election could lead to friction with Washington if new engagement with Pyongyang comes without any of the reciprocal nuclear disarmament progress that Washington demands from the North.
Moon and Park also agree on the need to fight widespread government corruption, strengthen social welfare, help small companies, close growing gaps between rich and poor, ease heavy household debt and rein in big corporations that have grown so powerful they threaten to eclipse national laws. They differ mainly in how far they want to go.
Moon wants to drastically expand welfare, while Park seeks more cautious improvement in the system, out of concern that expanding too much could hurt the economy, according to Chung Jin-young, a political scientist at Kyung Hee University in South Korea.
Both candidates also have promised to strengthen the alliance with the United States while boosting economic ties with China.
Park is aiming to make history as the first female leader in South Korea and modern Northeast Asia. But she also works under the shadow of her father, Park Chung-hee, who ruled South Korea as dictator for 18 years until his intelligence chief killed him during a drinking party in 1979.
Park's father is both an asset and a soft spot. Many older South Koreans revere his strict economic policies and tough line against North Korea. But he's also loathed for his odious treatment of opponents, including claims of torture and snap executions.
"Nostalgia for Park Chung-hee still runs deep in our society, particularly in the older generation," Chung said.
A Park win would mean that South Korean voters believe she would evoke her father's strong charisma as president and settle the country's economic and security woes, Chung said.
Moon, on the other hand, was a young opponent of Park Chung-hee. Before working for Roh, whom Lee replaced in 2008, Moon was a human rights lawyer. He also spent time in jail for challenging Park's government.
Moon's parents lived in the North Korean port city of Hungnam before fleeing to South Korea aboard a U.S. military ship in daring evacuation operations in December 1950, six months after the Korean War broke out.
Moon's parents lived in an interim shelter on South Korea's southeastern Geoje Island and later moved to a nearby village where Moon was born in 1953. Moon's father did manual labor at the camp while his mother peddled eggs.
A Moon win would be a clear judgment against the Lee government, said Hahm Sung Deuk, a political scientist at Korea University in Seoul. Moon's appeal is that he "appears to be nice, honest and clean."
Moon has been aided by Ahn Cheol-soo, a medical doctor-turned-software mogul who led Park in hypothetical two-way polls before he dropped out of the race last month. Ahn, who does not belong to any party, has thrown his support behind Moon since withdrawal.
With South Korea's economy facing a 2 to 3 percent annual growth rate for this year and the next, the presidential candidates have focused on welfare and equality and fairness issues. Neither, however, has matched Lee's campaign promise to boost South Korea's economy by an ambitious 7 percent growth annually, apparently aware of the global economic challenges that beset the country's export-driven economy.
Economic worries may be the focus of many voters, but North Korea forced itself as an issue in the closing days of campaigning with its rocket launch last week, which put a satellite into orbit.
The launch won't be a major election influence, but it will consolidate conservative votes in favor of Park, said Hahm. He said the launch will remind South Korean voters that "the North Koreans are unpredictable and belligerent."