But with little separating the party from conservative New Democracy, a coalition government is likely.
Syriza's leader, Alexis Tsipras, called the snap poll after securing a multi-billion euro international bailout.
Whoever is elected will have to oversee austerity measures demanded by Greece's creditors as part of the deal.
Syriza supporters' gathered in central Athens for the party's final rally on Friday, in what Mr Tsipas said sent "a message of determination and victory".
"On Sunday, we're facing a crucial referendum - to put an end to old political system, protecting oligarchs and corruption," he tweeted.
At the final New Democracy rally, its leader Vangelis Meimarakis attacked Syriza's "false promises" in the run-up to the last election, when it pledged to end austerity.
"It's high time we did away with incompetence. The Syriza experiment ends on Sunday," he said.
At a debate earlier in the week, Mr Meimarakis proposed forming a grand coalition with Syriza but Mr Tsipras rejected it as "unnatural".
Most of the parties support the bailout. But one of those that does not - the far-right Golden Dawn - is predicted to come third.
Analysts say the migrant crisis on Greece's doorstep may bolster support for Golden Dawn, which is vehemently opposed to immigration.
Final campaign rallies have been held in Greece ahead of Sunday's elections, with several polls giving left-wing Syriza a small lead.