Rafa Benitez's side came into the game on the back of a goalless draw with Brighton and Hove Albion on Saturday, which made their chances of beating the drop slimmer but they were able to make amends this time.
Atsu came close to scoring on two occasions in first-half but the midfielder saw his efforts go wide before he fired straight at Stoke goalkeeper Jack Butland following a DeAndre Yedlin's cutback.
Dwight Gayle replaced the Black Star by the 64th minute, with Newcastle eventually opening the scoring through Ayoze Perez in the 73rd minute.
What a positive way to start the year , massive 3 points 🙏🏿👍🏿 thanks for your support ⚫️⚪️ https://t.co/BVUFSO8Apn— Christian Atsu (@ChristianAtsu20) January 1, 2018
“What a positive way to start the year, massive three points thanks for your support,” Atsu wrote on Twitter.
The victory means Newcastle have now moved out of the relegation zone and sit 13th with 22 points.
They have also won back to back away Premier League matches for the first time since November 2014.