Black Stars midfielder,
Newcastle took the lead four minutes before the break as Atsu cut inside from the right to unleash an unstoppable strike.
Dwight Gayle and Jonjo Shelvey had chances to make it 2-0 and Dominic Ball hit the woodwork for the hosts late on.
Gouffran was unlucky not to put the Magpies ahead when his volley was blocked on the line by the chest of Ball, and Taylor had a decent chance for the Millers when his shot clipped the crossbar.