Coventry recorded their biggest win under Iain Dowie as Barnsley slipped back towards the drop zone.
Jay Tabb began a devastating spell of three goals in 11 minutes when he shot home from just outside the box.
Michael Mifsud steered home Marcus Hall's cross Dele Adebola drilled into the roof of the net from 12 yards.
Adebola outmuscled two Barnsley defenders to notch his his second just after half-time before Bobby Hassell headed in a 79th-minute consolation.
Coventry City manager Iain Dowie:
"I think Dele Adebola was almost unplayable.
"There is no question he is the strongest man in the world! You can't shift
him and he's got a good touch.
"It was a very, very pleasing display. This was always going to be a
difficult game and we had to make sure we started this game with a huge amount of respect for Barnsley."
Barnsley manager Simon Davey:
"I think we were beaten on the day by a better team. I felt the lads looked tired and we never looked in the game in any department.
"I am very confident we can beat the drop. There is a belief in the camp that
we will stay in the Championship.
"No matter what set-backs we get, and today is a set-back, we still have the
belief that we can go to any team and get a result."
Coventry: Marshall, Virgo, Hawkins, Ward, Hall, Osbourne (Birchall 72), Hughes, Doyle, Tabb (McKenzie 76), Adebola, Mifsud (Cameron 86).
Subs Not Used: Steele, Page.
Goals: Tabb 27, Mifsud 32, Adebola 38, 50.
Barnsley: Colgan, Austin (Hassell 52), Paul Reid, Nyatanga, Heckingbottom, Togwell, Howard (Nardiello 59), McCann, Ferenczi, Rajczi, Devaney (Kyel Reid 52).
Subs Not Used: Lucas, Eckersley.
Goals: Hassell 79.
Ref: M Russell (Hertfordshire).