Andre Boucaud gave the Magpies a 39th-minute lead, against the run of play, when he fired into the bottom corner from 30 yards after being given time to pick his spot.
Franck Moussa almost levelled for the hosts a minute later, but was thwarted by a low save from Bartosz Bialkowski, although he appeared to know little about it.
The Magpies looked the more likely after the break and Yoann Arquin doubled the lead five minutes from time with a fine curling effort.
Richard Wood pulled one back for Coventry with an 88th-minute header from a John Fleck corner, but despite a number of late chances and goalmouth scrambles they could not find an equaliser.
Lee Hughes came on as a second-half substitute for Notts County, returning to Coventry for the first time since he was jailed for his involvement in a fatal car crash near the city over eight years ago.