With all 260 electoral districts reporting on Sunday, Andreas Laemmel from Merkel's Christian Democrats won the contest for a seat in Dresden with 37% of the vote. He defeated Marlies Volkmer from Chancellor Gerhard Schroeder's party, who had 32.1%.
While the outcome of the Dresden vote does not significantly alter the results of the 18 September election, the strength of an extra seat in parliament is expected to give the conservatives a psychological advantage in coalition talks, which have been stalled because both Merkel and Schroeder claim a mandate to be chancellor.
Roland Koch, the conservative governor of Hesse state, said the vote confirmed the Christian Democrats and their Bavaria-only sister party, the Christian Social Union, as the strongest bloc in parliament, and it should choose the next chancellor.
"I see it as a step toward stability that we need to explain to the Social Democrats to stick to the rules," Koch said before final results were announced. "I see it as a signal for Angela Merkel."
More than 72.1% of those eligible in the East German district cast ballots, officials said after polls closed.
The high turnout reflected how seriously the 219,000 registered voters there were taking balloting.
"Mr Schroeder must finally understand that his time is up"
Guido Westerwelle, general-secretary, Free Democrats
The 18 September vote centred on different visions of Germany's role in the world and how to fix its sputtering economy.
Schroeder touted the country's role as a European leader willing to stand up to the United States, while Merkel pledged to reform the economy and strengthen relations with Washington.
Merkel and Schroeder have made exploratory talks over whether there is enough common ground between the two to form a so-called "grand coalition". The two were forced into the arrangement because neither won a majority.
Talks going slowly
Such a slow pace is frustrating other parties, such as the Free Democrats, who could try to build a government with the conservatives if a grand coalition fails.
"What can't be agreed upon in two weeks will not be any better in four weeks," Wolfgang Gerhardt, the parliamentary leader for the Free Democrats, said before Sunday's vote.
He criticised current plans to end negotiations as early as 31 October as being too late and not indicative of a government capable of bringing about reforms to create jobs and enhance Europe's largest economy.
Free Democrats general-secretary Guido Westerwelle celebrated the result, saying it should persuade Schroeder to drop his demand to be Germany's leader.
"It means that Mr Schroeder must finally understand that his time is up," Westerwelle said.