Major German parties have tended to determine their leaders without a contest, and this is the first open competition for the CDU leadership since 1971.
A third contender, Health Minister Jens Spahn, 38, an outspoken critic of Merkel's 2015 decision to welcome more than one million asylum seekers to Germany, is seen as being in a distant third place.
"We must have the courage to stay the course against the Zeitgeist", she said.
Friday's vote pits CDU general secretary Annegret Kramp-Karrenbauer, a Merkel ally, against Friedrich Merz, a former leader of the party's parliamentary group who stands for a more conservative approach and has been away from front-line politics for a decade.
Ms Kramp-Karrenbauer became the first woman to serve as a state minister for internal affairs in 2000 and the first woman to serve as prime minister of Saarland, a position she held from 2011 to 2018.
Dr Angela Merkel's Christian Democrats vote on Friday (Dec 7) to decide who replaces her as party leader and moves into pole position to succeed her as German chancellor.
A senior CDU official, speaking on condition of anonymity, said many delegates were undecided before the congress and could be swayed by how the candidates present themselves on Friday.
Playing up her experience in regional government, she added to cheers and loud applause: "I learned what it is to lead - and above all learnt that leadership is more about being strong on the inside than being loud on the outside". She has indicated she would implement tougher rules on migrants, telling a German newspaper that while she owes much to Merkel, they have different views on a number of issues, and criticising her predecessor's "lack of consistent explanation on migration policy".
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For years, Merkel's popularity lifted the CDU and its Bavaria-only sister party, the Christian Social Union.
She also celebrated Germany's balancing its budget in recent years and its response to the eurozone debt crisis. He won 157 votes.
Whoever wins will face towering challenges for the party, which is now drawing around 28 percent at the polls, far below the around 40 percent enjoyed during Merkel's heyday. Merkel's fourth-term governing coalition with the center-left Social Democrats has lurched through a series of crises since taking office in March, and the CDU has lost supporters both to the liberal Greens and the far-right Alternative for Germany.
"In hard times we shouldn't forget our Christian and democratic stance", she said.
"We are facing a turning point and need a breakthrough for the next years".
She said that "we kept a cool head" and "we showed everyone" by recovering.
"I wasn't born as chancellor or as party leader", she said.
She was given a 10-minute standing ovation with cries of "Danke Angie" to acknowledge her 18 years in the job.
Pointing to the rise of populism worldwide and what she called a breakdown of shared Western values, Merkel said the order she had championed was at risk.