Polls opened at 8:00 local time (06:00 GMT), with preliminary results due to be announced shortly after 18:00.
Chancellor Angela Merkel's conservative allies, the Christian Social Union (CSU), are tipped to prevail.
The CSU has ruled Germany's wealthiest state for 56 years with its "laptop and lederhosen" strategy - promoting hi-tech firms and local traditions.
At 3.8%, Bavaria has the lowest unemployment in Germany, where the national average lies around 6.8%.
The southern region is also home to some of the world's largest carmakers like Audi and BMW.
Bavarian Prime Minister Horst Seehofer, who leads the CSU, has described Bavaria as "the gateway to paradise".
'Penalty spot'
Latest polls suggested his party could receive at least 47%. Some 9.5 million people are eligible to vote in Sunday's ballot.
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A win would allow the CSU to regain the absolute majority in the regional parliament, lost in 2008 after the party's worst election results in six decades.
It would force out its coalition partner, the Free Democrats (FDP), and let the CSU govern alone again.
Importantly, a conservative victory could also provide a boost for the CSU's sister party, Chancellor Merkel's Christian Democratic Union (CDU) in the general election, correspondents say.
CSU lawmakers make up nearly a quarter of Mrs Merkel's centre-right bloc.
"We will sound the signal for victory nationwide," Mr Seehofer said.
"Dear Angela, we'll put the ball on the penalty spot, you just have to kick it in."
Mrs Merkel is campaigning for a third term in office in elections taking place on 22 September.
Her main challenge is from the centre-left Social Democrats (SPD), who are currently trailing behind in opinion polls.
SPD leader Peer Steinbrueck downplayed the significance of the Bavarian vote, saying that "the federal election isn't being decided here".
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