Strikers Shola Ameobi and Nile Ranger struck in either half to secure all three points at the Ricoh Arena.
Newcastle, looking to take advantage of West Brom's shock defeat 24 hours earlier, made a bright enough start without really threatening the Coventry goal.
The home side had to rely on some good defending, however, in the opening exchanges. Jordan Clarke did well in the 18th minute when he raced back to cut out a cross from Peter Lovenkrands.
He injured himself in the process and had to be replaced by fellow teenager Jermaine Grandison.
Martin Cranie then produced a last-ditch challenge to stop Jonas Gutierrez in this tracks as he prepared to turn the ball in from the by-line.
Coventry were working hard to hang on in midfield, but as they began to feel more secure they managed to post an attacking threat.
Aron Gunnarsson skipped his way round three challenges in the 27th minute before Stephen Taylor managed to halt his progress and when the ball fell to Jack Cork, his effort was blocked.
They then managed to hit the bar twice in a few seconds when Leon Best watched a shot strike the woodwork, before a follow-up header from Michael McIndoe was deflected on to the bar.
But then Ameobi showed his class to turn Leon Barnett and fire the visitors in front as the first half moved into injury time.
Coventry came out looking dangerous in the second half and could well have pulled level.
Freddy Eastwood was their main threat. He had one shot saved and just when he appeared to have found a way past Steve Harper, Ameobi managed to block his effort.
Cork and Gunnarson both threatened Harper's net, but in the end they fell short.
As Chris Coleman's men continued to push forward they began to look susceptible on the break and so it proved when sub Ranger tapped in to make the Magpies' victory safe.