In a lively clash at close quarters, Edwards accused Cheney of "not being straight with the American people" about the war, where he said U.S. casualties are rising monthly and the United States is bearing 90 percent of the cost and suffering 90 percent of the dead and wounded.
Cheney promptly challenged those figures, saying the Iraqi security forces had taken nearly half of the casualties.
"For you to demean their sacrifice is beyond the pale," he said to Edwards seated a few feet away.
"Oh, I'm not," Edwards protested before the vice president cut him off.
A CBS News poll of 178 uncommitted voters found that 41 percent said Edwards won the debate, versus 28 percent who said Cheney won. Thirty-one percent said it was a tie.
A majority of uncommitted voters came away from the debate believing that both men could be an effective president if needed. More of those surveyed (76 percent) said they liked Edwards personally than said they liked Cheney (53 percent).
Cheney, 63, and Edwards, 51, sat a few feet apart around a semicircular table on a stage at Case Western Reserve University. Gwen Ifill of PBS, moderator for the evening, faced them.
The debate format encouraged give-and-take, and neither the vice president nor Sen. John Kerry's running mate shrank from the task.
"Frankly, senator, you have a record that's not very distinguished," Cheney said to the North Carolina lawmaker after accusing him of a pattern of absences in the Senate during his one term.
Edwards summed up his points like the former trial lawyer he is.
In a jab at the Bush-Cheney campaign's claim on experience, Edwards said, "Mr. Vice President, I don't think the country can take four more years of this type of experience."
He also said that as a member of Congress more than a decade ago, Cheney voted against Head Start and banning plastic guns that can escape detection in metal detectors.
"This was not the vice-presidential debate that we saw in 2000 when you had the avuncular Cheney trading good natured barbs with a whimsical Joe Lieberman," said CBS News Chief Washington Correspondent Bob Schieffer.
"This was a very testy debate," Schieffer said. "The vice president tonight had the unfortunate task of defending a war that does not appear to be going very well these days on the very day that the former top civilian official in Iraq was making a speech saying that we went about it in the wrong way. That was a tall hill for the vice president to climb tonight, and he had to explain it as best he could."
Edwards was on the attack from the opening moments of the debate.
He said that in addition to mismanaging the war in Iraq, the administration had Osama bin Laden cornered in the mountains of Afghanistan at one point, but turned over the hunt for the mastermind behind the Sept. 11 terrorist attacks to Afghan warlords.
"The senator has got his facts wrong," said Cheney. "We've never let up on Osama bin Laden from Day One. We've actively and aggressively pursued him."
The vice-presidential debate took on increased importance as polls showed a tightening presidential race following a strong performance by John Kerry in his first debate last week with President Bush.
Apoll taken in the days after that debate found Kerry had gained ground and moved into a virtual dead heat with the president among likely voters.
On Tuesday night, Cheney noted that Kerry had opposed the first Persian Gulf War, and said it was "part of a consistent pattern over time of always being on the wrong side of the fence."
Cheney also said of Kerry, "I don't believe he has the qualities needed to be commander in chief."
Edwards said Cheney had previously suggested ties between the terrorists responsible for the terrorist attacks on Sept. 11, 2001, and Iraqi leader Saddam Hussein.
"You've gone around the country suggesting that there is some connection. There is not," Edwards said.
Edwards also said the connection between Saddam and the al Qaeda terrorist network was minimal or nonexistent. Cheney asserted Saddam's Iraq "had an established relationship with al Qaeda."
Edwards charged that Cheney, as the chief executive officer of Halliburton, pushed the U.S. to lift sanctions against Iran, did business with countries that were "sworn enemies of the United States,'' and that Halliburton paid millions of dollars in fines for providing false information – "just like Enron and Ken Lay."
Cheney accused Edwards of "trying to throw up a smoke screen" and said, "there's no substance to the charges."
Kerry and Edwards have sought to link Cheney to Halliburton as a symbol of corporate greed and insider connections. Halliburton has reported making more than $7.6 billion so far from U.S. government contracts in Iraq.
On domestic issues, Edwards said President Bush had presided over a loss of jobs during his administration – the first president to do so since Herbert Hoover sat in the White House during the Great Depression in the early 1930s. He also said more Americans are in poverty, and living without health insurance, than when the president took the oath of office in 2001.
But Cheney said jobs are being created, and said a Kerry-Edwards administration would seek to raise taxes.
Edwards denied that even before the vice president said it, noting that the Democratic proposal calls for rolling back the Bush tax cuts on only those earning $200,000 or more a year.
Cheney, whose daughter, Mary, is a lesbian, spoke supportively about gay relationships and said "people ought to be free to choose any arrangement they want." That position differs with President Bush, who supports passage of a constitutional marriage to ban same-sex marriage, and Cheney said, "He sets policy for this administration, and I support him."
Edwards said it was obvious that the Cheneys loved their daughter and that "you can't have anything but respect" for them. "I believe marriage is between a man and a woman and so does John Kerry," Edwards said. But, he added, "We should not use the Constitution to divide this country."
The debate was staged in Ohio, considered one of the top prizes in this election. With 20 electoral votes, the state went to Mr. Bush by 3.6 percentage points in 2000.