Las Vegas (CNN) Minnesota Sen. Amy Klobuchar first publicly vented her chief frustration with Pete Buttigieg nine months ago in a parking lot in Cresco, Iowa.

He is benefiting from male privilege and wouldn't be treated the same if he were a woman, she said.

"Could we be running with less experience," Klobuchar asked rhetorically of women in an interview. "I don't think so. I don't think people would take us seriously."

The then-South Bend, Indiana, mayor had barely risen to national attention at that point in the Democratic primary fight, but that sentiment -- that Buttigieg had not paid his dues and would be dismissed if he were a woman -- has gnawed at the Minnesota senator ever since. And it has only grown as Buttigieg has outflanked her for the moderate lane in the primary, rising to a top finish in Iowa and a strong second place finish in New Hampshire

While the feeling has been obvious in previous debates -- like when Klobuchar dismissed Buttigieg as a "local official" or dismissively compared him to President Donald Trump by labeling him the "cool newcomer" -- the senator's antipathy for Buttigieg burst into plain view Wednesday night here in Las Vegas.

When Buttigieg questioned Klobuchar's inability to name the President of Mexico in a recent interview, the senator shot back, "Are you trying to say that I'm dumb? Or are you mocking me here, Pete?"

When the former mayor slammed her for voting for Trump's Customs and Border Patrol head, the senator dismissively said, "I wish everyone was as perfect as you, Pete," before touting the fact she was "in the arena."

And in possibly the clearest sign of her distaste for the mayor, Klobuchar brushed off a Buttigieg handshake after the debate, walking away from the former mayor as he looked to do the customary -- albeit, awkward -- post-debate greeting.

The Klobuchar-Buttigieg clash has been brewing for months. The candidates are offering voters a similar vision: Both are looking to push back against the party's leftward lurch with more moderate policy proposals and are making an electability argument by urging the Democratic Party to remember the need to win back the Midwest, an area that Trump rode to victory in 2016.

The similarities are so clear to Klobuchar aides that they often grumble when Buttigieg uses similar phrases to the senator.

And a more heated clash looked inescapable after the Minnesota senator finished in a surprising third place in New Hampshire and raised enough money in the wake of the primary to extend her campaign even further than her top advisers initially believed.

But few operatives -- even those on each campaign -- believed it would get as intense as it did on Wednesday night, a fact that Democrats privately said stems from Klobuchar's belief that a 30-something year old woman mayor from a city of 100,000 in Indiana would not be taken as seriously as Buttigieg has been.

"She feels the whole thing deeply," Jess Morales Rocketto, a Democratic operative and political director at the National Domestic Workers Alliance, said after the debate. "It offends her that they are even mentioned in the same breath."

Rocketto added: "I relate to that. I think a lot of women do."

Christina Reynolds, a top official at Emily's List, a group that works to elect pro-choice women, said that with Klobuchar, "you saw some pushback against a candidate who has consistently argued that Washington experience either doesn't count or is the wrong kind of experience."

"As someone who has gotten quite a bit done in the Senate, she's got a lot to say about that," she added.

The crescendo of last night's clash was when Buttigieg took on Klobuchar for being unable to name the Mexican President in an interview last week.

"You're staking your candidacy on your Washington experience. You're on the committee that oversees border security. You're on the committee that does trade," Buttigieg said. "You're literally in part of the committee that's overseeing these things and were not able to speak to literally the first thing about the politics of the country to our south."

Buttigieg, during his answer, fully turned his body to Klobuchar, making clear he was taking her on -- directly.

And Klobuchar welcomed the open target.

"Are you trying to say that I'm dumb," she said. "Or are you mocking me here, Pete?"

The derision reared again later in the debate when Buttigieg faulted Klobuchar for voting for Kevin McAleenan, Trump's former head of Customs and Border Protection -- a debate that got directly to the heart of Buttigieg and Klobuchar's feud.

The mayor made the debate about Washington experience and Klobuchar's need to own up to her record.

"If you're going to run on your record in Washington," he said, "then you've got to own those votes, especially when it comes to immigration. ... You voted to make English the national language. Do you know what message that sends in as multilingual a state as Nevada to immigrants?"

Klobuchar's sarcastically shot back: "I wish everyone was as perfect as you, Pete. But let me tell you what it's like to be in the arena."

The line, which was greeted with audible "ohhs" from the audience, crystallized Klobuchar's view of Buttigieg -- that of a candidate new to politics with little experience and no record.

Voters at Buttigieg and Klobuchar events in New Hampshire and Nevada have told CNN that they are deciding between both Democrats, especially as former Vice President Joe Biden's level of support has fallen in recent weeks.

But what the clash on Wednesday night's debate stage made even clearer was the animosity between the two candidates -- something that did not subside once they the debate stage.

When Buttigieg was asked after the debate about his frequent exchanges with Klobuchar, the former mayor looked to deflect.

"I don't know where that comment came from," Buttigieg said of Klobuchar suggesting he thinks he is perfect. "I am far from perfect. Journalists remind me, politically speaking, I'm far from perfect every day."

But then he went back at Klobuchar: "If you are running on your experience in Washington, you should be prepared to defend the decisions you made and the votes that you took in Washington."

Klobuchar seethed even deeper after the debate.

After lamenting that the debate didn't focus enough on Trump -- "I hope in another debate, that we remember who's out there," she said -- the senator couldn't let a question about Buttigieg go unanswered.

"I made very clear that I think that we need someone leading the ticket that's actually won," she said as she made her way out of the debate venue. "And he ran for DNC chair and he lost, and he ran a statewide in the state of Indiana and he lost by over 20 points."

It's "going to be up to the voters of Nevada," she continued, "if they want to put our ticket in the hands of someone who has not yet won even a statewide race or a DNC race."

CORRECTION: This story has been updated to accurately state when the interview in which Klobuchar couldn't name the Mexican president took place.