New Nottingham Forest boss Steve Cotterill watched from the stands as his side slumped into the bottom two.
Lukas Jutkiewicz headed the only goal of the game in the 57th minute, just moments after Lee Camp made a brilliant save to deny Richard Keogh.
The well-taken goal secured Coventry only their second win of the season.
But their celebrations were muted after goalkeeper Joe Murphy was carried off on a stretcher following lengthy treatment.
Coventry boss Andy Thorn earlier confirmed his commitment to City after "unfounded and malicious" rumours he was set to quit and join Forest.
But he would have been less than impressed with his side's shaky start.
The Sky Blues threatened for the first time just before the half-hour mark as Clive Platt's looping header forced Camp to tip over the crossbar.
The second half continued to be a lacklustre affair until it suddenly burst into life after 10 minutes.
Forest's players felt the ball had crossed the touchline for a throw-in before Wes Morgan was forced to concede a corner. From the resulting set-piece, Camp produced a stunning save to keep out Keogh's header.
But Camp was powerless as another ball quickly came back into the area and Jutkiewicz was left unmarked to head home.
Clint Hill then headed Conor Thomas's effort off the line before Camp parried Bell's strike to safety.
With 20 minutes remaining, City goalkeeper Murphy collided in the air with Ishmael Miller and, after receiving lengthy treatment, was carried off to be replaced by Chris Dunn.
Forest substitute Robbie Findley nodded a good chance over from close range before Jutkiewicz headed on to the top of crossbar.
Despite 10 minutes of injury time because of the injury to Murphy, Forest were unable to find an equaliser.