Schulz, 61, outfoxed Merkel on ties with Turkey and bounced her into beefing up her rhetoric by vowing to stop Ankara's bid to join the European Union if he was elected chancellor.
According to a separate poll by Infratest Dimap for ARD television, Merkel came across as more competent, credible and likeable than Schulz.
In a pivot from her previous position, the centre-right leader declared on Sunday: "The fact is clear that Turkey should not become a member of the European Union". Merkel also stressed that she would stick to her longtime policy of choosing global cooperation over confrontation, including with U.S. President Donald Trump. "The Chancellor and the President expressed their support for a tightening of European Union sanctions against North Korea", the statement said.
"The chancellor and the president are in agreement that North Korea has trampled on worldwide law and that the global community must therefore react with determination against this new escalation", Merkel's office said in a statement after she spoke on the phone with Macron. "Whether we can win over all the countries for this I don't know".
Her show of experience appeared to work with voters. The only category where Schulz scored higher was for being more combative.
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Merkel has been chancellor since 2005 and is widely seen as Europe's most influential politician.
Schulz has called Merkel "aloof" and attacked her on a range of issues but failed to dent her lead.
Much of the debate was taken up with the issue of migrants, with Merkel saying she stood by her decision to allow hundreds of thousands of refugees into Germany in 2015 and insisted the country can't isolate itself from the effects of wars and poverty elsewhere in the world.
"Integration is not something that happens on paper", Schulz said. Merkel shot back: "We had a very dramatic situation then". She has previously said she would respect the talks. During the debate, both candidates refused to rule out continuing their current grand coalition at the national level after the election.