The visitors dominated proceedings pretty much throughout, hitting the frame of the goal three times and seeing opposition keeper Rob Elliot produce a couple of big stops.
In the end Sterling's volley just over half an hour in proved the difference, ensuring that City left the North-East with an 18th-successive league win under their belt.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Elliot; Yedlin, Lascelles, Mbemba, Dummett, Manquillo; Murphy, Diame, Shelvey; Aarons, Joselu
SUBS: Darlow, Clark, Merino, Atsu, Ritchie, Perez, Gayle
STARTING XI: Ederson; Walker, Kompany, Otamendi, Danilo; Fernandinho, Bernardo; De Bruyne, Gundogan, Sterling; Aguero
SUBS: Bravo, Mangala, Sane, Adarabioyo, Jesus, Toure, Diaz
Rafael Benitez: "We have been on a bad run but we have kept working hard and maintained belief. The victory has given us a big boost in confidence, and it will be good if we can now back that result up against City."
Pep Guardiola: "We must do what we have done until now - that is what we have to do, and focus on Newcastle. Focus on what we have to do on the pitch - defensively, offensively, individually, as a group."
NEWCASTLE UNITED SUBS: Darlow, Clark, Merino, Atsu, Ritchie, Perez, Gayle
MANCHESTER CITY SUBS: Bravo, Mangala, Sane, Adarabioyo, Toure, Diaz