Democratic vice presidential candidate Tim Kaine aggressively challenged Republican candidate Mike Pence over a long list of Donald Trump’s controversial positions and statements Tuesday night, drawing a vigorous defense of Mr. Trump’s tax history.

But Gov. Pence sidestepped criticism of Mr. Trump’s demeaning comments about women, his public doubting of President Obama’s citizenship and broader questions about his temperament.

The encounter between Gov. Pence of Indiana and U.S. Sen. Kaine of Virginia, who is the No. 2 to Democratic presidential nominee Hillary Clinton, was the only such debate between the vice presidential contenders before the Nov. 8 election, and the two spent most of their time attacking each other’s running mates.

For more than 90 minutes at Longwood University in Farmville, neither Gov. Pence nor Sen. Kaine appeared to deliver a knockout punch.

Gov. Pence sought to project an image as a reassuring presence, in contrast with the bombastic Mr. Trump, while Sen. Kaine tried to frighten voters away from Mr. Trump and make Mrs. Clinton seem more trustworthy.

A CNN/ORC snap poll declared Gov. Pence the winner with 48 percent support, compared with 42 percent for Sen. Kaine, who frequently interrupted his opponent.

Mr. Trump watched the debate from Las Vegas and in an unusual move, live tweeted during the debate and said he was pleased by his running mate’s performance.

“Mike Pence won big. We should all be proud of Mike!” Mr. Trump said.

The encounter set the table for a second presidential debate looming on Sunday, Oct. 9, at Washington University in St. Louis between Mrs. Clinton and Mr. Trump, who needs to rebound from a rocky performance from his first debate, one that gave Mrs. Clinton a boost in national opinion polls with Election Day only five weeks away.

Bickering Tuesday night between Sen. Kaine and Gov. Pence was so intense that they frequently talked over each other. Sen. Kaine was seen by television commentators as being over-prepared and over-eager as he circled back to Mr. Trump’s refusal to release his tax records at almost every opportunity.

Sen. Kaine called the Republican presidential nominee a danger to U.S. national security and someone who denigrates women and minorities and appears to pay little in federal taxes.

Sen. Kaine drew Gov. Pence’s ire by hearkening back to a remark from former Republican President Ronald Reagan that “some fool or maniac” with a nuclear weapon could trigger a catastrophic event.

“And I think that’s who Gov. Pence’s running mate is,” Sen. Kaine said.

Gov. Pence shot back: “Senator, senator, that was even beneath you and Hillary Clinton and that’s pretty low.”

Sen. Kaine repeatedly sought to persuade Gov. Pence to defend Mr. Trump’s positions, but Gov. Pence steadfastly refused to take the bait.

One of Sen. Kaine’s most aggressive lines of attack was over Mr. Trump’s refusal to release his tax records, a decision that breaks with the practice of all other presidential nominees in modern history.

The New York Times reported last weekend that Mr. Trump had taken a $916 million tax loss in 1995 and may have avoided paying federal taxes for 18 years because of it.

“Gov. Pence had to give Donald Trump his tax returns to show he is qualified to be vice president. Donald Trump has to give his tax returns to show he is qualified to be president,” Sen. Kaine said.

Gov. Pence defended Mr. Trump, saying the New York real estate developer had created thousands of jobs and had used federal tax laws as they were designed to be used.

“Why won’t he release his taxes?” Sen. Kaine fired back.

With the close White House race starting to tip in Mrs. Clinton’s favor, Gov. Pence outlined a detailed conservative agenda on tax policy, entitlements and immigration. He was markedly more prepared and more detailed in his answers than Mr. Trump was in the first presidential debate on Sept. 26. He was also more consistent in painting the Democratic ticket as career politicians unwilling to shake up Washington.

“Hillary Clinton and Tim Kaine want more of the same,” Gov. Pence said.

He also repeatedly accused the Democrats of running an “insult-driven” campaign — an ironic attack line given that Mr. Trump has leveled repeated insults against Mrs. Clinton and his former rivals in the Republican primaries.

There was a striking difference in the two men’s manner. Sen. Kaine, usually easygoing, went on the attack from the start, repeatedly interrupting and challenging Gov. Pence. Gov. Pence, an equally genial politician, was unflappable.

Sen. Kaine, too, defended his running mate’s weaknesses, chiefly the public’s questions about her honesty and trustworthiness. He said that while Mr. Trump was “selfish,” Mrs. Clinton had devoted her career to helping children and families.

Social issues were a bigger part of the conversation than in the first presidential showdown, reflecting both candidates’ religious faith.

Sen. Kaine, a Catholic who personally opposes abortion but has consistently voted in favor of abortion rights, said of the Republican nominee, “Why doesn’t Donald Trump trust women to make this choice for themselves?” He also pointed to Mr. Trump’s assertion that women should face some kind of “punishment” for abortion, a comment Mr. Trump later walked back.

Gov. Pence, raised Catholic but now a Protestant evangelical, stressed his opposition to abortion and said he was “proud to be standing with Donald Trump” on the issue.

On criminal justice, Sen. Kaine argued that Mr. Trump’s embrace of “stop and frisk” style policing was a mistake. Gov. Pence argued that Mrs. Clinton has used police shootings to argue that there is “implicit bias” in police departments, and he said the Democrats should “stop seizing on these moments of tragedy.”

Sen. Kaine quickly shot back: “I can’t believe you are defending the position that there’s no bias.”

While last week’s first presidential debate was watched by a record-setting television audience of 84 million people, Tuesday’s contest had an audience of about 35 million viewers.