Preferences will almost certainly decide whether the Greens' Cathy Oke or fellow Melbourne city councillor, Labor's Jennifer Kanis, replace ALP veteran Bronwyn Pike in the seat.
The Liberal Party is not running a candidate; it garnered more than a quarter of Melbourne primary votes at the 2010 state poll. The Greens won almost 32 per cent of primary votes at the last state election, while Labor managed more than 35 per cent.
Ms Oke is the favourite and will become the Greens' first lower house MP in the Victorian parliament if she wins the by-election.
Labor has held the seat, which includes Carlton, Flemington, North Melbourne and the Docklands, for more than a century.
Ms Oke said she hoped her efforts in running a positive campaign focused on local issues would pay off.
"We'll be creating history here in Melbourne if we have a lower house representative," she told reporters in North Melbourne.
"But I don't underestimate how close it's going to be."
State Opposition Leader Daniel Andrews said voting Labor would strengthen the ALP's chances of defeating the coalition at the 2014 state election.
"It's a clear opportunity for Melbourne voters to send the strongest, the most definitive message to Ted Baillieu that on TAFE and in so many other areas, he's gone too far," Mr Andrews said.
Ms Pike held Melbourne by a margin of about six per cent.
Vote counting will begin soon.
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