The French striker and his side had been second best for long spells, yet they left with a win after a rousing if fortuitous recovery against luckless visitors.
An Everton defender was adjudged to have made contact just outside the area in a separate incident.
The French forward soon reached double figures for the campaign when he bundled home George’s delivery to the far post.
The Everton captain appeared to pull an opponent’s hair and raise an arm towards another’s face during the contest.
Home fans produced a smattering of boos when Everton trudged off at half-time.
Coventry coped comfortably for much of the opening period and finished the first half on top.
The visitors finally, and deservedly, took the lead after benefiting from abysmal Everton defending.
Team and striker had defied expectations. Coventry, for all their first-half control, left empty-handed.
There was no questioning the legitimacy of Barry’s next involvement.
That second strike completed the turnaround and fired Everton to the win.