Here are key moments from the face-off between Republican vice-presidential candidate Mike Pence and Democratic rival Tim Kaine at Longwood University in Farmville, Va. (Sarah Parnass/The Washington Post)

Donald Trump and Hillary Clinton weren’t on the stage at the vice-presidential debate here Tuesday night, but it didn’t really matter. They were still front and center.

Stripped of the overpowering personalities of Trump and Clinton, the debate between Sen. Tim Kaine (D-Va.) and Indiana Gov. Mike Pence (R) offered the possibility of a more civil and sober conversation about issues that divide the two national party tickets. At times it was just that, whether on the economy, immigration, the chaos in the Middle East or abortion.

But for much of the evening, it was a boisterous proxy war by a pair of running mates whose goal was to take down the other’s presidential nominee. They squabbled, they disagreed, they interrupted one another, they rolled out canned lines, and they feigned indignation.

It was bad enough almost from the start that, barely a third of the way through the 90-minute debate, moderator Elaine Quijano of CBS News admonished the candidates to back off. “The people at home cannot understand either one of you when you speak over each other,” she said.

Overall it was an unsatisfying, disjointed debate, as the two candidates brushed past specific questions to open up other arguments at will. It probably changed few minds and no doubt brought some encouragement to the bases of the two parties. In that way it was a typical vice-presidential debate.

Mike Pence and Tim Kaine sparred over the issue of abortion during the vice-presidential debate at Longwood University in Farmville, Va., Oct. 4. (The Washington Post)

Both Kaine and Pence understood their objectives. Kaine’s was to hurl Trump and everything he has said in Pence’s face and force him to respond. He began by using an opening question about preparedness to be president, pivoting to a series of attacks on Trump.

Pence’s role was to do what Trump could not do consistently during the first presidential debate, which was to prosecute a case against Clinton — highlighting both her policy vulnerabilities as secretary of state and questions about her private email server and the Clinton Foundation. He was more effective by far than Trump, but he struggled to fully defend everything Trump has said and done.

Kaine accused Trump of running an “insult-driven, selfish, me-first” campaign. Pence took umbrage at that. “You and Hillary Clinton would know a lot about an insult-driven campaign,” he said, and then launched into a catalogue of complaints about Clinton, President Obama and the state of the world under the two of them.

With that, the evening on the campus of Longwood University seesawed back and forth; occasionally there was serious policy discussion, but then it was quickly back to barbs and insults. Kaine was by far the more aggressive debater, overly so in the opening as he appeared almost too eager to make the entire evening about Trump.

Pence appeared taken aback by the assault, though he surely understood that it would be coming. More disciplined than Trump, and with a baritone voice that evoked a sense of seriousness, he battled back.

Were it not for the landmines Trump had left for Pence to tiptoe through, it might have been a different debate. Pence pressed at every opportunity to raise questions about Clinton, questions that Trump failed to raise at the first debate.

But Kaine kept returning to Trump, daring Pence to defend his decision not to release his taxes; to praise Russian President Vladimir Putin; or to explain Trump’s comments about women, Mexicans and others.

Throughout the campaign, Pence has walked a line between being loyal to the man who put him on the ticket and protecting his own political future. That was the case again Tuesday night, though it’s likely he did more to help himself than to absolve Trump of the charges Kaine kept leveling.

At times he simply sought to deny that Trump had said or done things Kaine brought up, whether in calling for the deportation of the roughly 11 million undocumented immigrants or praising Putin as a stronger leader than Obama.

Kaine was far more ready, even eager, to take on criticism of Clinton, jumping at the chance to compare the Clinton Foundation with Trump’s charity. Whether his style sat well with undecided voters, those few who are still making up their minds, is another question.

In Pence and Kaine, the public got a glimpse of two politicians — though of different parties and ideologies — who bear more resemblance to one another than any comparison of Trump and Clinton. Both are lawyers, and both have served in Congress and in governor’s mansions.

Both have low-key personalities, and neither is known for slashing, negative politics, though the traditional role of a vice-presidential candidate is to carry the attack against the other party’s presidential nominee. They were little known nationally when chosen as running mates to the two least-popular major-party nominees in the history of polling.

Pence had the more difficult task Tuesday night, forced to take the stage after Trump suffered through one of the worst weeks of his candidacy — a week that began with the Hoftstra debate, where polls declared Clinton the winner, and that spiraled downward from there.

The damage to Trump was mostly self-inflicted, starting the morning after the debate with insults of a former Miss Universe and followed by an early-morning tweet storm that extended the controversy. Then came a New York Times exclusive that revealed that Trump had claimed $916 million in losses on his tax returns during the 1990s and, that same night, a rambling, off-script performance at a rally.

Trump’s week was his worst since immediately after the Democratic convention, when he got into a verbal exchange with a Gold Star family; that, combined with Clinton’s convention bounce, put the Republican ticket behind in the polls by the end of August. The effect of the past several days was that Trump appeared to arrest the gains he had been making in the polls before the first debate, if not begin to reverse them.

Four years ago, Vice President Biden had to follow a weak performance by President Obama, who lost his opening debate against Mitt Romney. Biden’s challenge, however, was not as difficult as Pence’s. Biden needed only to reenergize a Democratic base demoralized by Obama’s performance.

He did that with a display of aggressiveness — some critics judged it over the top — that contrasted with Obama’s laconic posture against Romney in Denver. Biden did not have to answer for or defend controversial behavior on the part of the president.

Still, it was left to Obama to produce the real rebound in the second of the three presidential debates, just as it will be Trump’s challenge to deliver a more consistent and focused performance against Clinton when the two meet at Washington University in St. Louis on Sunday night for a town hall debate.

Vice-presidential debates rarely matter. They can produce memorable video clips, as several have over the years, but they don’t move the polls. Pence played his prescribed role Tuesday night, delivering what Trump hoped for. But so did Kaine, as he kept Trump’s vulnerabilities front and center.

Given the damage Trump did to himself over the past seven days, that will put much greater pressure on the Republican nominee Sunday to show that he learned from his mistakes in the first debate and to show the voters a more disciplined candidate.