ARD and ZDF television exit polls showed the Merkel-allied Christian Social Union, traditionally the dominant force in the prosperous southern region, winning 49% support.

That’s enough to win back an absolute majority in the state legislature that the CSU lost in 2008. But the polls gave Mrs Merkel’s national governing partners, the pro-market Free Democratic Party, only 3% support – meaning they would lose their seats.

Germany’s main opposition party, the Social Democrats, finished a distant second with about 21% – better than the post-Second World War they hit five years ago, but far too little to give them any hope of unseating the conservatives. And their allies, the Greens, lost ground to score 8.5%.

“It’s a great day for the CSU,” said Mrs Merkel’s agriculture minister, Ilse Aigner, a member of the party – which has led Bavaria since 1957, most of the time with an absolute majority.

The Social Democrats of Mrs Merkel’s challenger, Peer Steinbrueck, pointed to the positive; general secretary Andrea Nahles said it was a good result by Bavarian standards and noted that hers was the only opposition party to make gains.

Mrs Merkel, who is favoured to win a third four-year term next Sunday, has benefited from Germany’s strong economy and low unemployment.

That’s even truer in Bavaria, the tradition-minded homeland of retired Pope Benedict XVI and also a high-tech and industrial centre, where nearly 9.5 million people are eligible to vote. Its jobless rate is just 3.8%, the lowest of any German state and well below the national average of 6.8%.

Still, the Free Democrats’ weakness is a concern for Mrs Merkel. They’re also weak in national polls, and today’s outcome opens up the possibility of Merkel supporters switching their support to the smaller party to ensure that it tops the 5% support needed to keep its seats in the national Parliament – which could weaken her conservatives.

“Those who want Angela Merkel must vote for Angela Merkel,” Armin Laschet, a deputy leader of the chancellor’s Christian Democratic Union, told ARD television. The Free Democrats “will make it,” he added.