The Sky Blues took the lead after just two minutes, with Liverpool loanee Ryan Kent scoring his first senior goal by cutting in from the left wing before finishing with a curling effort.
Newcastle loanee forward and League One top scorer Adam Armstrong then scored Coventry's second after 18 minutes by smashing in an Aaron Phillips cross, giving the 18-year-old his 11th goal of the season.
Lee Johnson's side fell to another Coventry goal just minutes later, however, when Armstrong finished for his second goal of the game with a clinical strike after being released by a Jim O'Brien flick.
The two-goal lead failed to last long for the home side at the Ricoh Arena, with Scowen scoring Barnsley's second of the night moments later after getting in behind the Coventry defence.
Former Chelsea, Liverpool and England international midfielder Joe Cole then added to the scoreline, curling in a free kick from 25 yards out to restore a two-goal advantage.
The game looked to be over, but there was more drama as Barnsley were awarded a stoppage-time penalty when Aaron Phillips was deemed to have handled the ball. Scowen stepped up to the spot and scored his second of the game, but it was too late to halt Coventry's victory.