The three points helped ease the pressure on under-fire manager Micky Adams as his side recorded its first victory in six matches.
Both teams went into the game struggling for form and the match predictably started scrappily.
Plymouth had the first real chance of the game in the 11th minute, with captain Paul Wotton meeting Tony Capaldi's free-kick with a free header which went narrowly wide.
A lovely move 23 minutes later say involving David Norris play a one-two with Micky Evans but his shot was wide.
But two minutes later Norris was not to denied as he opened the scoring, beating Marton Fulop with a lovely half-volley.
Right-back Anthony Barness got to the by-line and crossed the ball, which was met by Norris to score his first of the season.
Things went from bad to worse for Coventry as three injuries forced the Sky Blues to use all their substitutes in the 27th minute.
Richard Shaw, Andy Impey and Don Hutchison replaced injury victims Matt Heath, Marcus Hall and James Scowcroft.
But the Sky Blues hauled themselves back in to the game with a lovely goal in the 36th minute thanks to a wonderful run by Claus Jorgensen.
The Faroe Islands international beat two men on the right hand side with a jinking run before supplying an inviting cross which Andy Morrell converted.
The goal gave Coventry new belief and Adebola went desperately close to giving his side a half-time lead as he struck the underside of the bar with a right-foot shot.
But in the fourth minute of injury time, Coventry were not to be denied thanks to a debut goal from Hutchison.
The former Liverpool midfielder collected a cross from Andy Impey, turned Mathias Doumbe before firing past Romain Larrieu in the Plymouth goal.
Three minutes after the break, Coventry scored again as Gary McSheffrey scored his eighth goal of the season.
The 23-year-old collected a poor clearance from Hasney Aljofree and tucked the ball into the bottom right-hand corner.
Wotton almost pulled one back just minutes later but his 30-yard piledriver went just over the top.
But the goal seemed to knock the stuffing out of Plymouth as they struggled to find their first-half form.
With Coventry content to defend their two-goal lead, the game ended as it began - a scrappy affair.