Adebola met Gary McSheffrey's cross with 25 minutes to go to cancel out Dean Ashton's first-half opener.
Ashton, who had gone close with a testing 25-yard free-kick, climbed high to head in Dean Marney's centre.
Leon McKenzie drew a save from Stephen Bywater as Norwich had the best chances and Ashton should have won it when he headed against the bar late on.
Coventry manager Micky Adams:
"He made a couple of great saves and generally his calmness and handling were just what we needed.
"We expected a tough game. Norwich are one of the favourites but we did okay.
"That's a point no-one expected us to get. It's given us a foundation to play on and if we stay injury-free we won't be a pushover for anyone."
Norwich: Green, Louis-Jean, Fleming, Doherty, Drury, Marney (Thorne 80), Hughes, Charlton (Jarrett 88), Huckerby, Ashton, McKenzie.
Subs Not Used: Ward, Brennan, Colin.
Booked: Fleming, Doherty.
Goals: Ashton 21.
Coventry: Bywater, Duffy, Page, Heath, Hall, McSheffrey (Jorgensen 87), Doyle, Hughes, Scowcroft, John, Adebola.
Subs Not Used: Ince, Morrell, Osbourne, Shaw.
Booked: Doyle, Duffy.
Goals: Adebola 65.
Att: 25,355
Ref: R Beeby (Northamptonshire).