"I know you're under a lot of duress to make up for lost ground, but I think people would be better served if we don't interrupt each other," Ryan later scolded his rival, referring to Democratic pressure on Biden to make up for President Barack Obama's listless performance in last week's debate with Mitt Romney.
There was nothing listless this time as the 69-year-old Biden sat next to the 42-year old Wisconsin congressman on a stage at Centre College in Kentucky.
Nearly 90 minutes after the initial disagreement over foreign policy, the two men were still at it, clashing sharply over rival approaches to reducing federal deficits.
"The president likes to say he has a plan," said Ryan, a seven-term congressman. But in fact "he gave a speech" and never backed it up with details.
Biden conceded Republicans indeed had a plan. But he said that if enacted it would have "eviscerated all the things the middle class care about," including cutting health care programs and education.
As Biden and Ryan well knew, last week's presidential debate has fueled a Republican comeback in opinion polls.
Republicans and Democrats alike have said in recent days the presidential race now approximates the competitive situation in place before the two political conventions. Obama and Romney are generally separated by a point or two in national public opinion polls and in several battleground states, while the president holds a slender lead in Ohio and Wisconsin.
With Democrats eager for Biden to show the spark the president lacked, he did so. He supplemented his criticism by periodically smiling mockingly, wagging his finger and raising his arms in mock disbelief as his rival spoke.
Ryan, sitting on the national debate stage for the first time, settled on a smirk for parts of the debate. He sipped water and cleared his throat through many of Biden's answers.
Unprompted, Biden brought up the video in which Romney had said 47 percent of Americans pay no federal income tax, view themselves as victims and do not take responsibility for their own lives.
"It's about time they take responsibility" instead of signing pledges to avoid raising taxes, Biden said - of Romney, Ryan and the Republicans.
Ryan was ready with a response. "This is a man who gave 30 percent of his income to charity, more than the two of us combined," he said of the man at the top of the Republican ticket. "Mitt Romney's a good man. He cares about 100 percent of Americans in this country. And with respect to that quote, I think the vice president very well knows that sometimes the words don't come out of your mouth the right way."
The serial disagreements started immediately after the smiles and handshakes of the opening.
Ryan said in the debate's opening moments that U.S. Ambassador Chris Stevens had been denied sufficient security by administration officials. Stevens died in a terrorist attack on the U.S. Consulate in Benghazi on Sept. 11.
"Not a single thing he said is accurate," Biden shot back.
Both the president and Romney campaigned in battleground states during the day before ceding the spotlight to their political partners for the evening.
"I thought Joe Biden was terrific tonight. I could not be prouder of him," Obama told reporters after watching the debate aboard Air Force One.
Likewise, Romney called Ryan and congratulated him on his performance, a campaign spokesman said.
Obama and Romney hold their next debate on Tuesday in Hempstead, N.Y, then meet again on Oct. 22 in Boca Raton, Fla.
In Kentucky, Biden and Ryan seemed ready for a showdown from their opening moments on stage, and neither seemed willing to let the other have the final word. They interrupted each other repeatedly - and moderator Martha Raddatz of ABC as well.
With Democrats eager for Biden to show the spark the president lacked, he did so.
Ryan focused on dreary economic statistics - 23 million are struggling to work, he said, and 15 percent of the country is living in poverty. "This is not what a real recovery looks like."
Medicare was a flashpoint, as well. Ryan said Obama's health care plan had diverted $716 billion from the program for seniors and created a new board that could deny care to patients who need it.
Democrats "haven't put a credible solution on the table," he said. "They'll tell you about vouchers. They'll say all these things to try to scare people."
Biden quickly said that Ryan had authored not one but two proposals in which seniors would be given government payments that might not cover the entirety of their care. Otherwise, he said, the Romney-Ryan approach wouldn't achieve the savings they claimed.
Unlike Obama, Biden had no qualms about launching a personal attack on Romney.
After Ryan argued that Romney's plan would pay for reduced tax rates by eliminating tax loopholes for the wealthy, Biden noted that on a recent interview on CBS' "60 Minutes," Romney defended the 14 percent tax rate he pays on his $20 million income as fair, even though it's a lower rate than some lower income taxpayers pay.
"You think these guys are going to go out there and cut those loopholes?" Biden asked, addressing the national TV audience, his tone of voice indicating he did not.
But Ryan said he and Romney believe "taking 28 percent of families' and businesses' income is enough."
"What we're saying is lower tax rates across the board and close loopholes primarily on the higher income people," Ryan said. He said that instead of specifying what loopholes and other tax breaks would be eliminated, Romney preferred to lay out broad principles in hopes of reaching a bipartisan agreement.
Across 90 minutes, the two men agreed precisely once.
That was when Ryan, referring to the war in Afghanistan, said the calendar was the same each year. Biden agreed to that, but not to his rival's underlying point, which was that it was a mistake for Obama to have announced a date for the withdrawal of the remainder of the U.S. combat troops.
The fiercest clash over foreign policy came in the debate's opening moments, when Ryan cited events across the Middle East as well as Stevens' death in Libya as evidence that the administration's foreign policy was unraveling. The Republican also said the administration had failed to give Stevens the same level of protection as the U.S. ambassador in Paris receives.
Biden rebutted by saying that the budget that Ryan authored as chairman of the House Budget Committee had cut the administration's funding request for diplomatic security by $300 million.
On the nation's economy, both men were asked directly when his side could reduce unemployment to 6 percent from the current 7.8 percent. Both men sidestepped.
Biden repeated the president's contention that the nation is moving in the right direction, while Ryan stated the Republican view that economic struggle persists even though Democrats had control of both houses of Congress during the first two years of Obama's term.
"Where are the 5 million green jobs" we were told would be created? Ryan said to Biden.
Obama campaigned in Florida during the day. Mocking recent changes in Romney's rhetoric, he told a rally in Miami rally, "After running for more than a year in which he called himself severely conservative, Mitt Romney is trying to convince you that he was severely kidding."
Romney visited with 93-year-old Billy Graham in North Carolina before speaking to an evening rally in Asheville, N.C. "Prayer is the most helpful thing you can do for me," he told the evangelist.
For Biden, Thursday night's debate was his first since the 2008 campaign, when he shared a stage with Sarah Palin, then John McCain's running mate.
Ryan spars frequently with Democrats during debates on legislation on the House floor and in the House Budget Committee, which he chairs, but not in a one-on-one encounter covering 90 minutes and a virtually unlimited range of topics.
For all their differences, the two men shared a common objective, to advance the cause of their tickets in a close race for the presidency. And they appeared to avoid any gaffes that might forever seal their place in the history of debates.