For the second season running goals from Stephen Hughes and Dele Adebola had put Coventry in control, but Derby hit back in the closing minute to save themselves from what would have been a third consecutive defeat.
Even so this was not a convincing performance from Derby whose vulnerability at the back and in midfield was again exposed.
The Sky Blues will wonder how they allowed the game to slip away and Derby will need to perform much better against fierce rivals Nottingham Forest next week.
The Rams made several changes after last week's defeat at Preston but Coventry always looked capable of opening up their defence.
Hughes struck the first blow in the 22nd minute when he scored with a low shot from the edge of the area after Pablo Mills had failed to clear a cross convincingly.
Coventry wasted other chances before the interval and Derby had to reshuffle again when Michael Johnson was forced out of the action with a mouth injury.
They had a chance to equalise when Grzegorz Rasiak headed narrowly wide in the 69th minute but Coventry appeared to have won the game 11 minutes later.
Two dreadful mistakes from Richard Jackson and Tom Huddlestone allowed Adebola to escape and drive a right-foot shot into the roof of the net.
County reduced the deficit in the 88th minute then Morten Bisgaard set up Rasiak, who struck a low shot into the bottom right corner from 10 yards.
When the fourth official indicated four additional minutes, Coventry were rattled and Paul Peschisolido punished them when he finished confidently after Rasiak sent him clear.