Kevin Kyle, Julian Gray and Michael Mifsud scored second-half goals as Coventry started the season with a deserved win at Barnsley.
Leon McKenzie headed home a free-kick to put Coventry ahead but it was his handball that led to Brian Howard equalising from the penalty spot.
Kyle put the Sky Blues back ahead with a header from Jay Tabb's cross, who later passed for Gray to score.
And Tabb then picked out Misfud, who drove the ball past Nick Colgan.
Barnsley manager Simon Davey:
"It was a bad start for us.
"I felt that for an hour we played well and we finished the stronger side in the first half.
"I am disappointed to lose 4-1, it's not acceptable the way they caved in and the players have been told that.
"When their second went in we caved in a bit. We lost a bit of heart."
Coventry manager Iain Dowie:
"We wanted a good start.
"Barnsley were very competitive in the first half and it's not an easy place to come to.
"For me it was a tough game. At half-time I wanted us to kick on.
"At 2-1 up some of our football was pleasing but I always felt that they could get a goal back."
Barnsley: Colgan, Souza (Werling 73), Nyatanga, Reid, Kozluk, Devaney, Howard, Johnson (Togwell 73), Ricketts, Mostto (Odejayi 60), Ferenczi.
Subs Not Used: Letheren, McCann.
Goals: Howard 9 pen.
Coventry: Konstantopoulos, Borrowdale, Ward, Hall, Osbourne, Gray, Doyle, Michael Hughes (Stephen Hughes 81), Tabb, McKenzie (Best 72), Kyle (Mifsud 72).
Subs Not Used: Marshall, Hawkins.
Booked: Osbourne, Mifsud.
Goals: McKenzie 6, Kyle 50, Gray 65, Mifsud 90.
Ref: S Mathieson (Cheshire).