While opinion is divided, Mrs Clinton is largely thought to have come out on top in Sunday's debate in St Louis. But columnists raised the issue of her failure to tackle Mr Trump effectively, allowing him to "exceed expectations".
"The smiling Hillary we saw throughout the first debate on Long Island? She didn't make the trip west."
Fox News concludes that Mr Trump managed to pull off a surprising performance, although the news channel does not explicitly state that the Republican candidate won the debate.
The conservative network says he performed well, pivoting and manoeuvring through questions, allowing him to save his presidential hopes.
Political analyst William Whelan said the night fell into the hands of Mr Trump.
He said the Republican defended his record and unlike the first debate, when he was often blown off course by the former secretary of state and "torpedoed by his own badgering performance", he improved as the night went on.
Mr Trump's decision to launch a blistering attack against Hillary Clinton and her husband is described by Fox as the equivalent of "Hillary dropping Alicia Machado on Trump" in the previous debate.
That was the line used by Breitbart news, which is in a minority in handing the title to Mr Trump.
In a leading story quoting comments from former mayor of New York City, Rudy Giuliani, it reports that Mrs Clinton was "pounded on bad decisions".
It refers to accusations from Mr Trump that Mrs Clinton and the Democratic Party helped "create the vacuum in the Middle East" that allowed so-called Islamic State to form.
The hard-right news website, whose executive chairman Stephen Bannon was appointed Mr Trump's campaign chief in August, is running its own readers' poll, the results of which have yet to be announced.
The site also highlights support from Republican vice-presidential nominee Mike Pence, who said in a tweet that he was proud of Mr Trump and congratulated him on "a big debate win", while ending it with a shortened form of Mr Trump's 'Make America Great Again' slogan.
"All Hillary Clinton had to do was remain upright for 90 minutes."
The Washington Post's verdict is that the debate highlighted an "increasingly isolated" Mr Trump during an "unusually dark and bitter face-off". Over the past year, the newspaper has been at the forefront of investigations into Mr Trump, and has published several editorials condemning the candidate.
On the news site's Right Turn blog, Jennifer Rubin says Mrs Clinton had very little to do in order to go "the last little way in wrapping up the election".
She writes that Mrs Clinton handled the audience well when answering questions, adding that the former secretary of state effectively won the debate early on by "simply keeping her cool".
Issues ranging from Mr Trump's tax payments to his foreign policy have, according to the Post, given Mrs Clinton plenty of material for a new raft of political ads.
In a separate piece for the Post, opinion writer Eugene Joseph Dionne Jr writes that Mr Trump's "petulant" and "boorish" approach on the night was an indication of "a man aware that his campaign was at the edge of extinction".
"It took the nastiest, most bitterly personal presidential debate in recent memory for the Republican nominee to stanch the downward plunge" - so writes Stephen Collinson for CNN.
He says that Mr Trump will live to fight another day "after throwing out a battery of vicious counter punches", while US politics "changed in the course of one nasty night".
Meanwhile a CNN/ORC poll of debate watchers handed Sunday's victory to Mrs Clinton. But the results also showed that Mr Trump managed to exceed expectations.
Mrs Clinton took the win with 57% of the vote, the poll says, while Mr Trump managed to achieve 34%. The result could be considered a disappointment for Mrs Clinton, who scored 62% in the first presidential debate.
The Atlantic, which endorsed Mrs Clinton last week, suggests that Mr Trump suffered an "implosion" in St Louis on Sunday.
Ron Fournier, whose coverage of US politics dates back to the days of Bill Clinton, writes that Mrs Clinton did about as well as anyone could while dealing with a "barking" opponent and "pouting menace".
Mr Fournier said that throughout the debate the controversial Republican "failed to patch together his collapsing campaign".
The website suggests that Mrs Clinton perfectly handled Mr Trump's comment about "instructing my attorney general to get a special prosecutor" to look into allegations that she deleted thousands of emails in violation of a congressional subpoena.
Mrs Clinton laughed and said it was a good thing "somebody with Donald Trump's temperament" doesn't have such power.
"Nothing hurts a bully like somebody laughing at him," the column says.
The US media have given their verdict on who won the second presidential debate after Republican Donald Trump and Democrat Hillary Clinton engaged in attack and counter-attack.