The managerless Magpies were holding the in-form Sky Blues heading to half-time until Danny Haynes was shown a straight red card in the 41st minute for a high tackle on Jordan Clarke.
This changed the game and the hosts - who were deducted 10 points at the start of the season - took full advantage.
Leon Clarke opened the scoring in the 49th minute, firing in off the bar from 12 yards after Blair Adams' perfect cut-back.
Clarke doubled the lead eight minutes later when he latched on to Mark Fotheringham's poor back pass to advance and chip over Bartosz Bialkowski.
And Callum Wilson added a third in the 64th minute when he collected John Fleck's ball over the top and rounded the keeper - matching Clarke's season tally of 11 goals.
County remain in the bottom four while Coventry have won three consecutive league games for the first time in three years and are unbeaten in six.