But surveys ahead of the vote showed the centre-left party running neck-and-neck with Ms. Merkel's CDU, with some even placing the CDU ahead.
Chancellor Angela Merkel's party secured a decisive win in a crucial State election, exit polls showed on Sunday, in a devastating blow to her main rival, the Social Democratic Party (SPD), four months before a national vote.
Merkel's conservatives in the state, led by challenger Armin Laschet, a liberal-minded deputy leader of the Christian Democrats, have little to lose after a awful showing in the state vote five years ago.
But she insisted that "the national election campaign is only beginning now". "So that we can forget those 50 plus years that the SPD is in power", said one older man.
Last weekend, they were beaten by German Chancellor Angela Merkel's party in Schleswig-Holstein in Germany's far north. After the SPD announced it was putting former European Parliament President Schulz up against Merkel at the beginning of the year, the party initially surged in national polls but has fizzled since. But defeats in two other state elections since late March punctured the party's euphoria over Schulz's nomination.
Schulz is hoping that his push for "social justice" will resonate in North Rhine-Westphalia, which has lagged behind western Germany economically. In the state's last election in 2012, the Social Democrats beat the CDU by 39.1 percent to 26.3 percent. The SPD are now junior partners in Germany's governing coalition.More news: Celtics seek top pick, Lakers aim to keep theirs in lottery
The projections put support for the pro-business Free Democrats, who are eyeing a return to the national parliament at September, at a strong 12 percent.
Kraft has ruled NRW since 2010 in a coalition with the environmentalists Greens, whose support among voters has more than halved to just over 6 percent, making it difficult for the SPD to muster a coalition, especially as their natural partners, the hard-left Die Linke, are also on 6 percent.
The likeliest outcome appears to be a "grand coalition" of the biggest parties led by whoever finishes first. The region of 17.9 million, almost a quarter of Germany's population, includes Cologne, Duesseldorf and the Ruhr industrial area.
Merkel's conservatives sought to portray Kraft's government as slack on security, and also assailed what they said is regional authorities' poor handling of education and infrastructure projects.
Asked about Germany's government after September her chief of staff, Peter Altmaier, said that "we always have to keep a cool head. we shouldn't talk about coalitions before the harvest is in".
That would mirror Merkel's national government, in which the Social Democrats are the junior partners.