Scholz's centre-left SPD won around 31 percent against the anti-immigration and anti-Islam AfD, which scored about 29 percent, according to the projections by public broadcasters on Sunday.
The result in the formerly communist east offers a rare moment of respite for Scholz's embattled coalition government, which has sunk in opinion polls a year ahead of national elections.
Despite its ballot box success, the AfD is unlikely to take power in any state since all other mainstream parties have so far ruled out entering into a governing alliance with the party.
Party co-leader Tino Chrupalla hailed the AfD's strong showing and noted that while they aimed to send Woidke into retirement, the results still reflected significant support.
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