This was a clash of the SPL's two form sides. Caley Thistle, this year's shock side, are already within touching distance of the top six, while Celtic, who hammered Dunfermline 6-0 on Saturday, knew they had to win to keep the frighteners on Rangers.
Home manager Craig Brewster left himself on the sidelines, his recurring knee knock keeping him out of the entire pool. Celtic's two injury fears however - Thompson and John Hartson - did make Martin O'Neill's starting 11. Injured Chris Sutton however did miss out.
It was a game to fire the imagination with history of two huge cup wins over Celtic still fresh in everyone's minds.
The first effort arrived after just 28 seconds when midfielder Roy McBain tested Rab Douglas from distance.
Celtic controlled the play for a while, but were kept out by Inverness' battling back line. Hartson threatened from long range too but his drive was deflected wide.
Aiden McGeady was looking lively on the right flank and his delivery was headed over the top by Stilian Petrov. Douglas was called into action again when a speculative shot from Graham Bayne was held, but gave him a moment's fright.
The majority of the first half was all about hard work and endeavour but chances were in truth few and far between.
Douglas was first to be tested after the break but he dealt well with a cross from Ross Tokely. At the other end, a rasping free-kick from Thompson forced a wonderful diving save from Mark Brown.
Action raged from end to end for a spell with the Highlanders battling all the way and Celtic seeking inspiration from somewhere. It almost came from the boot of Bellamy when he went on a searing run but his drive was saved by Brown.
Then Barry Wilson hit a snap-shot just over the bar as the ball broke to him. However, Bellamy finally broke the deadlock in the 61st minute when he linked with McGeady before finishing off a swift and smart move.
The Welshman could have made it two when his pace took him away from Stuart Golabek but he shot into the side-netting.
The game was settled with seven minutes to go when Grant Munro tripped Bellamy as he stole into the box to win a penalty. Thompson - cool as you like - slotted home to make the final score 2-0.