Their spirited back and forth on "New Day" went on for a half an hour -- and was at time pointed but always respectful. Cuomo sometimes challenged Giuliani on his facts and the former mayor pushed back.
What sparked the faceoff was Trump's latest blast accusing Obama of being the "founder" of ISIS and Hillary Clinton its "co-founder" -- both clearly inaccurate when taken literally. But Giuliani defended that comment at the opening of a lengthy battle with Cuomo.
"I think what he's saying there is legitimate political commentary," Giuliani said on "New Day." "Before Obama, ISIS was an almost unknown, small little organization. ... And here's why it happened: because he withdrew the troops from Iraq."
Giuliani also went to bat for Trump on his comments Tuesday where he appeared to say that people should consider shooting Hillary Clinton.
"You don't give him a fair shot. You take his words and you parse them and you take them apart," Giuliani told Cuomo, making it clear that he meant the media generally, not Cuomo himself. "I was on the plane with him when they called him and said to him, 'they're accusing you of saying 'Kill Hillary Clinton.' He said, 'What? I didn't say that.'"
Giuliani then compared Trump's comments to a remark Clinton herself made in the 2008 campaign justifying sticking around because Bobby Kennedy wasn't assassinated until June 1968.
"You know what she did after she said that? She apologized," Cuomo said."Well, because she was wrong," Giuliani replied.
Cuomo fired back, "Why didn't he (Trump) apologize?"
"Because he wasn't wrong!" Giuliani said.
Cuomo interjected, "How was he not wrong? To encourage people to use the Second Amendment, which means they have guns, that maybe you can do something?"
Then Giuliani deflected away from Trump, "Chris, Chris, Chris, Chris. He didn't encourage them to do that. He was saying don't vote for her. It's the Clinton spin machine."
In another exchange, Giuliani accused the media of ignoring the father of Orlando gunman Omar Mateen who attended a Clinton rally this week. But Cuomo quickly corrected him.
"That's not true, they've been all over the campaign asking," Cuomo said.
"Her answer was, 'Thank you.' Her answer was, 'Thank you," Giuliani said.
Cuomo shot back, "No. You just said, Rudy, she hasn't been asked. The answer is that's wrong. She has been asked."
Throughout the interview, Giuliani deflected questions about Trump. When he was pressed on Trump's decision not to release his tax returns, Giuliani put it back on the Clinton emails and argued that the issue was being ignored.
"It is nothing in comparison to the 35,000 emails that she destroyed," Giuliani said.
But Cuomo quickly cut him off: "Except we had a dozen different official investigations of that issue, it's not like we ignored the email situation, right? She gave 11 hours of open testimony on it. So it's not like nobody knows anything about it."
Even as Giuliani was alleging media bias against Republicans -- saying he experienced when he was mayor of New York City -- he told Cuomo that he comes on his show because Cuomo treats him fairly and is a stand up guy.
"You think I was treated fairly as the Republican mayor of New York City?" Giuliani asked Cuomo.
The CNN host said that was Giuliani's "truth" but not necessarily "the truth."
"It's absolutely true," Giuliani fired back. "I don't think that the overwhelming majority of your profession is fair."