The Yellows dominated possession but were caught on the break by Lenell John-Lewis who fired in spectacularly from 25 yards just before the interval.
Pat Hoban rewarded Oxford's dominance when he turned and fired-in the equaliser in the 72nd minute.
But County almost claimed all the points when Aaron Collins had a shot blocked in stoppage time.
Newport stay in 21st position, but are now unbeaten in eight league and cup games under manager John Sheridan, while Oxford remain second, two points behind Plymouth.
Oxford United manager Michael Appleton told BBC Radio Oxford:
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"The result was frustrating, but the second-half performance I thought was magnificent.
"We've had some good performances here recently, but the second half I thought they were outstanding.
"We got the one goal, very unfortunate not to find the second, but I couldn't have asked any more from them.
"The whole place just seemed a little but flat in the first half and I asked them to get on the front foot a bit quicker and it looked really exciting after the break.
"Newport are a side that John Sheridan's got well-organised, they came here tonight to get the point they wanted and it was a fantastic finish for them.
"Sometimes you've got to hold your hands up when someone puts one in the stanchion from 30 yards."
Newport manager John Sheridan:
"I think Oxford were the better side and put us on the back foot for a lot of the second half, but I was very pleased with the way we played first half.
"It's a good point because they are going well. I just think that if we believed ourselves a little more and we were brave and we took care of the ball a little bit more we could have caused them more problems.
"It's just about having a bit of game know-how and seeing the game through. But we gave the ball away cheaply and you end up on the back foot."

The firm, which controls two-fifths of the Scotch whisky industry, reported Scotch sales down 5% by volume.
However, single malts from Scotland continued their rise, led by the Singleton in the US and Taiwan.
American whiskey sales were also strengthened by apple-flavoured bottlings.
The London-based company has lost momentum due to slowing growth in key markets, including South America and China.
It has had lower shipments, as wholesalers have pulled back on stock-holding.
Despite flat comparable sales, Diageo posted a rise in pre-tax profits - from £2.7bn to £2.9bn. A big increase in volume of sales was driven by the acquisition of United Spirits in India, which boosted reported net sales by 5%.
Currency movements had an impact on its results, most significantly the Venezuelan bolivar and the Russian ruble. That cut £370m from sales and £100m from operating profit, once translated into sterling.
Some markets saw Diageo facing tough price competition, including Smirnoff vodka in the US and Johnnie Walker whisky in Brazil.
Notable improvements in sales were reported for Johnnie Walker in Mexico, while Guinness returned to growth in its UK and Irish home market.
American Blonde Lager drove Guinness sales up in the US. Net sales were up 6% in Africa.
Other developments during the financial year included a buyout of the remaining half of the Don Julio tequila brand, the sale of Gleneagles hotel and resort in Perthshire, and a shifting of strategy in South Africa to focus on spirits.
Diageo chief executive Ivan Menezes said the performance reflected the company's sales challenges, and that further changes were under way to sharpen the business.
He added: "We have consistently applied a long-term perspective in making changes, despite the short-term challenges we have faced from an external environment where currency volatility continues to impact the emerging market consumer."
He claimed the current financial year would see volume of sales improve, rising to about 5% organic sales growth from 2017, with improved margins.
Oxford missed a chance to go top of League Two when they were held at home by resurgent Newport.
[NEXT_CONCEPT]
Global drinks company Diageo has released full-year trading figures showing comparable sales remained flat for a second year.