Over 31 percent of voters in Baden-Wuerttemberg opted for the Greens led by Cem Ă–zdemir , a poll for broadcaster ZDF said, compared with 30.5 percent for the CDU. ARD, another public broadcaster, put the Greens ahead with 32 percent to 29 percent.
Both polls showed the far-right Alternative for Germany almost doubling its result compared to 2021 elections, taking third-place with about 18 percent of the vote.
The state-wide vote was seen as a test for German Chancellor Friedrich Merz's centre-right CDU, which had hoped to win the leading position in Baden-Wuerttemberg's government. The election was the first of several state elections this year in which the CDU hopes to stem the rise of the far-right Alternative for Germany (AfD).
The AfD did manage the biggest increase in voter share, roughly doubling its result compared with 2021 elections, and to take third place with about 18.7 percent of the vote.
If confirmed, it would be the party's best ever result in a west German state, beating the 18.4 percent gathered in 2023 elections in Hesse.
Baden-Wuerttemberg's neighbour, Rhineland-Pfalz, votes in a couple of weeks and September will see a series of regional votes in ex-communist eastern Germany, where the AfD can expect to perform well.
'Avoiding' key issues
Manuel Hagel, a 37-year-old former bank manager, led the CDU in the campaign and hit a rough patch after an eight-year-old video emerged in which he commented on female students' appearances after a school visit, earning condemnation from across the political spectrum.
Speaking after exit polls emerged, Hagel thanked his family for their patience.
"I would like to thank my family, especially my wife, because, frankly speaking, the last few weeks have been an enormous strain on my wife, my family and me personally," he said.
The Greens' candidate, Ă–zdemir, 60, is now likely to become Germany's first state premier of Turkish heritage, subject to coalition negotiations.
"The next chapter won't be one that we write by ourselves but rather with a coalition partner," he said.
"It will be, it has to be a partnership of equals," he added.
The AfD's likely result is its record in Baden-Wuerttemberg but behind the 25 percent it polls nationally.
On Friday, Merz attended the CDU's final campaign rally and said the vote would be watched outside Germany to answer the question: "Is the CDU still able to win elections, even when in government at such a turbulent time?"
A prosperous part of Germany that is a bastion of the country's ailing automotive industry, Baden-Wuerttemberg was for years a stronghold of the conservative CDU.
Polls showed that the economy was the most important topic for voters by some distance but not everyone thought it was taken seriously.
Brian Fuerderer, 34, the head of a local company making surgical equipment, told AFP ahead of the vote that he had found the electoral campaign "weak".
The parties were "avoiding the most essential issue... the economy" as well as the country's dependence on foreign energy supplies, thrown into stark relief by the Middle East war.
Merz has repeatedly promised to boost Germany's moribund economy and to that end lobbied the EU to weaken its ban on new combustion-engine cars after 2035.
Even the Greens' Ă–zdemir has said there should be more flexibility in the transition to electric vehicles.
Ă–zdemir has a national profile in Germany, having become one of the first MPs of Turkish origin in 1994 and serving as agriculture minister under former SPD chancellor Olaf Scholz.
The AfD's lead candidate, Markus Frohnmaier, has attracted national attention for his links to Russia and US President Donald Trump's Make America Great Again (MAGA) movement.
Speaking shortly after exit polls, Frohnmaier said the results showed there was a clear "conservative majority" in Baden-Wuerttemberg.
But the CDU, in common with Germany's other major parties, refuses coalitions with the AfD, considering it a dangerous far-right force.
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