The Reds had failed to score more than once in their previous 10 League Two games, but were dominant against Warren Feeney's side.
County striker Scott Boden opened the scoring at the wrong end when his header beat Joe Day after 36 minutes.
Shamir Fenelon then headed home eight minutes after the break, before Newport's Medy Elito was sent off with five minutes left for two yellow cards.
"It was disappointing, I don't think we got going from the first whistle, we couldn't get into a rhythm and our passing was poor," Newport manager Feeney told BBC Radio Wales.
"We have to put it to bed and move on to the next game, we are still in a fantastic position to avoid relegation and that is still my aim.
"You have ups and downs in a season and this was a down, the worst performance since I have been the manager. No-one likes to get beaten."

Called My Brother's Keeper, his new initiative aims to overcome the socioeconomic conditions keeping such youth from thriving.
The White House said businesses had pledged $150m (Â£89m) to promote it.
The president said it was an "outrage" that black and Hispanic men in the US fared so much worse than white men.
"I believe the continuing struggles of so many boys and young men - the fact that too many of them are falling by the wayside, dropping out, unemployed, involved in negative behaviour, going to jail, being profiled - this is a moral issue for our country," Mr Obama said at the White House on Thursday, with more than a dozen black and Hispanic young men and boys standing behind him.
"It's also an economic issue for our country."
In a memorandum released on Thursday, the White House said the task force would focus on issues facing boys and young minority men under the age of 25.
America's first black president has generally avoided policies defined by race, the BBC's Beth McLeod reports from Washington DC, but in an emotional speech Mr Obama said it was an outrage that young Hispanic and African-American men have the odds stacked against them in US society.
President Obama said young men from this group were more likely to have no father in the house, end up behind bars, or become victims of violent crime.
The White House has cited the relatively high unemployment rate for black and Hispanic men over the age of 20 and a higher-than-national-average poverty rate for minority households.
"We've become numb to these statistics, we're not surprised by them, we take them as the norm," Mr Obama said.
"We just assume this is an inevitable part of American life, instead of the outrage that it is.
"But these statistics should break our hearts. And they should compel us to act."
He spoke of visiting a school near his home in Chicago and sharing with the boys there his own experience of growing up without a father, acknowledging to them that he had been angry about that and had made "bad choices" and "got high without always thinking about the harm that it could do".
"I could see myself in these young men," Mr Obama told the audience at the White House. "And the only difference is that I grew up in an environment that was a little bit more forgiving, so when I made a mistake the consequences were not as severe."
Mr Obama's new initiative calls for foundations and community groups to co-ordinate investment in support programmes to keep young Hispanic and black men in school and away from crime.
A public online portal called What Works will provide access to data about such programmes.
To start the programme, a new federal task force will look at several issues affecting young men.
These include access to childhood support, grade school literacy, pathways to university and careers, as well as interactions with the criminal justice system and violent crime.
President Obama earlier met with foundation and business leaders and senior government officials to discuss the initiative and to thank them for their support.
According to the White House, business leaders have already invested $150m and plan to invest another $200m in the project over the next five years.
Senior White House adviser Valerie Jarrett described the effort earlier on Thursday as the beginning of a life-long endeavour for Mr Obama and his wife Michelle.
Ms Jarrett told US media it was a "moral, social responsibility that they feel will transcend the time that he's president".
Crawley completed a double over Newport County with a comfortable 2-0 victory.
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US President Barack Obama has called for a national campaign to improve opportunities for black and Hispanic boys and young men.