More than a million people are expected to vote at 1700 election-day sites before 6pm on Saturday to decide who will govern for the next four years.
Speaking shortly after voting opened, Mr Andrews said he was urging Victorians to opt for a "strong, stable, majority Labor government" as polls pointed to the potential for a hung parliament.
When pressed on his position on working closely with the Greens or independents to form a minority government, Mr Andrews said his position had been clear for more than a decade.
"No deal will be offered and no deal will be done," he told ABC TV.
Liberal Leader Matthew Guy, who steered the opposition to a crushing defeat at the 2018 election, said he was confident of victory despite the polls strongly favouring Labor.
"I am confident that Victorians will, at the end of the day, opt for a new government and a fresh start," he told reporters after casting his vote in Templestowe on Saturday morning.
Mr Guy said this year's election had a very different feel to the poll four years ago and voters were "genuinely looking for an answer to the woes of our health system", which they trusted the coalition to fix.
Almost half of the 4.4 million enrolled Victorians have already cast their ballot at early voting centres or via post, leading to a warning from the state electoral commission that this could delay results on election night.
The premier broke with tradition to cast his ballot early on Thursday evening, voting outside his electorate of Mulgrave alongside wife Catherine and two of his children.
On Saturday morning, Mr Andrews instead visited a level crossing removal site at Glen Huntly in a nod to one of his pet policies in government.
The premier appears in the box seat to win an elusive third term after a Newspoll published on Friday night showed Labor on track to return despite a swing against it of almost three per cent.
Labor leads the coalition 54.5 per cent to 45.5 per cent on a two-party preferred basis, according to the poll published by The Australian.
Labor starts on 55 lower house seats and would need to shed 11 to lose its grip on power. Newspoll has it on track to keep 45 to 50 seats.
The coalition has 27 seats and must pick up an extra 18 to govern outright.
However, the latest Resolve poll indicated Labor could lose between eight and 12 seats, putting it in danger of slipping into minority government.
In a final pitch to voters, Victorian Greens leader Samantha Ratnam promised more affordable housing and stronger action on climate change.
"Thousands of voters are saying they feel like major parties are ignoring some of the biggest issues bearing down upon them," Ms Ratnam told reporters in Brunswick.
Former Labor premier Steve Bracks said the polls indicated there had been a late surge towards the government, but the results were likely to be patchy across the state.
"Clearly in some of Labor's heartland, we'll see some bigger swings against Labor - probably not enough to lose the seats, not many seats," he told Sky News.
Mr Bracks agreed the premier was a polarising figure, saying about half of the electorate "actually love him" while the remainder wanted to get rid of him.
Independent consultancy RedBridge Group forecasts Labor to end up with between 41 to 48 seats and the coalition to finish in the range of 27 to 33 seats.
Among the Labor seats at risk of tumbling are Melton, Werribee, Point Cook, Hawthorn, Box Hill, Northcote, Richmond and Albert Park.
