Biden was the aggressor in the substantive head-to-head with Ryan, trying to make up for what many perceived as a lacklustre debate by the president.
Biden was more animated than Ryan, often interrupting to get his point across. But it wasn't clear whether it resonated with voters.
Many analysts commented on what appeared to be a dismissive or indignant smirk that Biden repeatedly flashed in response to some of Ryan's comments.
David Steinberg, the University of Miami's director of debate, said "both candidates did a really good job" and accomplished important debate goals, including to "personify the ticket leader's wisdom in picking them.
"Of course that's more important for Ryan to appear competent and he certainly did. [Another goal was to] bring unique and important competencies to the table which I think they both really did."
A CNN poll following the debate found that 48 per cent of those surveyed thought Ryan won, compared to 44 per cent for Biden. Yet a CBS News poll found 50 per cent thought Biden was the winner, compared to 31 per cent for Ryan.
'The debate was all about Joe Biden'
"I think the debate was all about Joe Biden," Todd Graham, director of debate at Southern Illinois University, told CBC News. "Joe Biden was strong, and then Joe Biden may have gone overboard after that, and then he was back to calm and sort of strong again."
Graham said he believed Biden, for the first 45 minutes, "ran over Paul Ryan in a particularly effective way.
"He just seemed he was more believable, he understood his arguments better, he talked about the middle class better, he talked about the 47 per cent and it just seemed like Paul Ryan seemed like one of those high school debaters. They're so young, so smart, and they don't do anything wrong, but they don't do anything to make you believe they have life experience."
But he said after that period, he felt Biden went over the top, only to rein it in later.
Joel Goldstein, a St. Louis University law professor, told CBC News that both men did well, but that Biden accomplished the most important task — changing the narrative from Obama's debate last week with Republican presidential candidate Mitt Romney.
"It will stop the angst in the Democratic base. The Democratic base will feel good about this and will contribute to some energy," Goldstein said. "I think it will change the discussion away from the first debate. For a couple of days this will be the topic then people are going to focus on Tuesday [the next presidential debate]."
Ryan slams 'unravelling' of Obama foreign policy
The combativeness began early with a question about the recent deadly attacks on the U.S. Embassy in Libya. Ryan slammed the Obama administration for first claiming that protesters incensed at an anti-Prophet Muhammad YouTube video were responsible, but then changing the story to say it was a terrorist attack.
Ryan also lashed out at the White House, saying it did not provide enough security and that the attack was indicative of a broader problem, namely "the unravelling of the Obama foreign policy."
Biden responded that "with all due respect, that's a bunch of malarkey." Biden said they went by what the intelligence community told them — that the attacks were a result of the YouTube video. He also said that the administration was not told they wanted more security there.
On Iran, Ryan accused the White House of having initially blocked attempts to impose tough sanctions against the country.
But Biden rejected that claim and shot back that the sanctions now in place "are the most crippling sanctions in the history of sanctions, period. Period."
Biden highlights Romney's '47 per cent' remark
Turning to the economy, Biden credited the president for cutting taxes on the middle class, helping people refinance their homes and rescuing General Motors. He accused Romney of wanting to let "Detroit go bankrupt" and "foreclosures hit bottom."
"But it shouldn't be surprising for a guy who says 47 per cent of the American people are unwilling to take responsibility for their own lives," Biden said, in reference to Romney's comments, captured on video at a fundraiser, in which he said that nearly half of Americans consider themselves victims and are dependent on the government
Ryan countered that the economy is "barely limping along," growing at only 1.3 per cent.
"We're heading in the wrong direction — 23 million Americans are struggling for work today. Fifteen per cent of Americans are living in poverty today. This is not what a real recovery looks like."
Ryan added that Romney, who gave 30 per cent of his money to charity, cares about 100 per cent of Americans.
"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," Ryan said, in reference to Biden's well-known verbal gaffes.
"But I always say what I mean," Biden shot back. "And so does Romney."
Attack dog or man's best friend?
The two also verbally sparred over Medicare and whether Romney supported a voucher system, prompting Ryan to snap: "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 keep interrupting each other."
They also went back and forth on taxes, with Biden saying Romney's plan to cut taxes 20 per cent across the board will actually result in a tax increase on the middle class, who will lose certain deductions.
While Biden said their plan was "not mathematically possible," Ryan said it had been done before, adding that John Kennedy lowered tax rates.
"Oh, now you're Jack Kennedy?" Biden said.
They also argued over the 2014 troop withdrawal date from Afghanistan and the hot-button issue of abortion.
Steinberg said that in these vice-presidential debates, the combatants can either be the attack dog or the "loyal best friend" dog.
"Biden did a great job of being the attack dog. Doing that, you sacrifice a little bit of likability and perhaps you don't sway too many undecided voters at least in the moment but you certainly reinforce and reinvigorate the people who are already with you.
"And I thought Ryan was more the other, the loyal supporter of his candidate and their policies."
The next two presidential debates are Tuesday in New York state and Oct. 22 in Florida.