Merkel was some 14 points ahead of Martin Schulz in opinion polls before the debate.
"I'll speak to my (EU) colleagues to see if we can reach a joint position on this so that we can end these accession talks", Merkel added.
Her overall performance was viewed as more convincing by 55%, compared to 35% for Mr Schulz, in a survey by Infratest Dimap for ARD television.
According to another survey carried out by the ZDF channel, Merkel won by 32 per cent against Schulz, who secured 29 per cent, while the other 39 per cent said they saw no differences between the two candidates.
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's strong words against Turkey came after her rival, Schulz, had minutes earlier called for an end to the European Union membership talks for Ankara. She has previously said she would respect the talks. "But I think one must say in the clearest terms that for us, there can only be a peaceful diplomatic solution".
She has weathered storms over mass immigration and financial and political turmoil in the European Union, while the SPD, Germany's oldest party, has struggled to promote a strong rival.
Chancellor Angela Merkel was forced to defend her response to the 2015 refugee crisis today in a TV debate ahead of Germany's federal election this month. Merkel called it a "very dramatic situation" that forced her to make a decision.
But with nearly half the voters still undecided three weeks before the elections, the straight-talking Schulz had been pinning his hopes on the prime-time TV showdown, hoping to sway millions to his cause and halt a devastating popularity slide.
"Integration is not something that happens on paper", Schulz said.
In the opening exchanges, Merkel rebuffed the moderators' suggestion that her backing for sovereign bailouts to preserve the euro area and her refusal to close Germany's borders at the height of the refugee crisis two years ago fueled the revival of the anti-immigration Alternative for Germany party.