Adebola's early second-half header was enough to wrap up three priceless points for Micky Adams' men against high-flying Luton at the Ricoh Arena.
Coventry should have taken the lead in the fourth minute. James Scowcroft dummied a pass from skipper Stephen Hughes to leave Gary McSheffrey in plenty of space inside the box. The unmarked striker turned and wastefully blazed a shot high over the bar from ten yards.
But Luton, who have proved they are made of stern stuff following their promotion from League One, hit back five minutes later with an equally good chance.
Kevin Nicholls floated in a free-kick from the centre circle which defender Chris Coyne headed back from the right byline. However, powerful striker Steve Howard somehow hit his shot onto the roof of the net.
In a close and combative affair at the Ricoh Arena, the next chance fell to Mike Newell's team. Warren Feeney latched on to a long pass from Coyne and the Northern Ireland international fired a shot over the bar.
Coventry's defence became stretched at times as they were hit on the counter-attack by the visitors and Michael Doyle showed his frustration when he was shown a yellow card in the 22nd minute for persistent fouling.
The hosts were awarded a free-kick following Marcus Heikkinen's foul on McSheffrey. Claus Jorgensen stepped up to drive a shot from the left wide of Marlon Beresford's left hand post.
Hughes was then booked in the 28th minute for bringing down Nicholls.
Nicholls touched the resulting free-kick to Dean Morgan but his effort from 25 yards did not trouble Coventry's debutant keeper Marton Fulop, who was signed on Friday on a three-month loan from Spurs.
Following a quiet spell in the game, Luton carved out a chance when Peter Holmes hit the side-netting with a shot from inside the six-yard box.
Scowcroft threaded a lovely pass through to McSheffrey to run on to and he twisted past Coyne and Carlos Edwards but his shot was charged down.
Jorgensen picked out Adebola in space on the left but his cross was cleared by the alert Heikkinen before McSheffrey could pounce.
It was Coventry who made the breakthrough in the 47th minute when the home team made their first shot on target count.
Scowcroft out-paced Edwards to whip over a cross from the right to Adebola at the far post and the giant striker headed the ball home from six yards.
Town responded immediately and could have equalised when Nicholls' left-wing cross found Holmes, but his effort hit a post.
The Sky Blues might have stretched their lead in the 54th minute when McSheffrey's great pass dropped at the feet of Adebola. The goalscorer raced forward and unselfishly laid the ball into the path of Doyle but Beresford saved his low drive with his legs.
The tempo of the match increased as Luton searched for an equaliser and City went forward in search of a decisive second goal.
Fulop needed to be at full stretch to tip away Feeney's angled cross-shot from the left and the same striker missed a good chance when he steered his angled shot wide.
Jorgensen's pass dropped to Adebola inside the box but the striker was unable to get enough power on his shot to turn the ball past Beresford, to round off Coventry's best display for weeks.