Rangers made two changes from last weekend with Kirk Broadfoot and Lee McCulloch replacing the injured Madjid Bougherra and Aaron
Both sides were conservative in the opening exchanges - although Referee Dougie McDonald did speak to both Aidan McGeady and Scott Brown for late tackles in the early stages.
Brown was the first to threaten - surging forward in 24 minutes only to see his 25-yard shot flash over
Five minutes later Glenn Loovens' header from a Shunsuke Nakamura free-kick was just wide of the target
Celtic were making the running in these early stages - McGeady skinning Steven Whittaker on the half-hour before seeing his cross volleyed over by Brown.
Rangers came more into the game as the interval approached - Steve Davis slicing his shot over the bar following a Sasa Papac lay-off from a Whittaker cross in forty minutes.
Just before the break Kyle Lafferty tested Artur Boruc when he cleverly chested down a Kirk Broadfoot cross before firing in an eighteen-yard shot that the 'keeper turned wide.
Rangers were now beginning to test the Parkhead defence - Davis had a chance in fifty minutes from a Kenny Miller pass only to drag his shot wide.
Nacho Novo made a welcome return from injury eight minutes later when he replaced Miller - and within sixty seconds the Ibrox men almost snatched the lead when Stephen McManus' pass-back to his goalkeeper was woefully short - Lafferty almost nicking the ball off of Boruc's toes.
Celtic were perhaps the more dangerous at dead-balls - Nakamura's 22-yard free-kick being touched wide by Allan McGregor in 62 minutes.
Seven minutes later the 'Gers 'keeper beat out Scott Brown's angled drive.
Loovens came even closer from the resultant Nakamura corner when his header was cleared off the line by Pedro Mendes.
Three minutes later a lightning break saw Mendes release Novo who cut inside before seeing his eighteen-yard shot turned over by Boruc.
McCulloch headed the resultant Mendes corner over - then sixty seconds later the turning-point of the match arguably arrived when Rangers' most effective player Lafferty was inexplicably replaced by Kris Boyd.
Mendes came close to breaking the deadlock in 81 minutes when his twenty-yard shot from a Barry Ferguson pass was just over.
Rangers suffered a body blow immediately thereafter when McCulloch limped off to be replaced by Christian Dailly who was making his first appearance for six months.
The ninety minutes ended goalless - and thus to extra-time.
It was all too clear that the first goal would be crucial - and Celtic it was who struck in the opening minute when Nakamura's free-kick was headed home by Darren O'Dea who had lost his marker - none other than the ineffective Boyd.
Celtic were now in the ascendancy as their fans polluted the Mount Florida atmosphere with sickening racist and sectarian songs and chants.
Two minutes after opening the scoring Scott McDonald should have made it two when he seized on a long ball miss-headed by Broadfoot - only to prod the ball wide of the target, then in the next attack Georgis Samaras shot over from a Brown lay-off
Brown himself might have sealed the win in 96 minutes when his twenty-yard shot from a Nakamura pass was touched over by McGregor then four minutes later the 'Gers 'keeper blocked Samaras as the Greek forward homed in on goal.
There was an unsavoury incident in 102 minutes when Celtic coach Neil Lennon assaulted Barry Ferguson at a throw-in - incredibly the Referee took no action whatsoever.
McGeady - already on a yellow card for a foul on David Weir - should have been ordered off in 106 minutes when he blatantly dived as he was tackled by Whittaker. Dougie McDonald however bottled the decision.
Rangers ran out of time - and were caught on the counter-attack in the dying seconds when McGeady streaked away before again blatantly diving to win a penalty and cause Broadfoot to be red-carded
Just to add insult to injury it was the winger himself who slotted home the spot-kick and Celtic had secured the League Cup.
Afterwards Walter Smith reflected
"It was a tight affair with defences and midfield cancelling each other out. There were few goalscoring opportunities. The opening goal was always going to be crucial. Tiredness eventually affected the game"
CELTIC Boruc; Hinkel, Loovens, McManus, O'Dea [Wilson 105]; Hartley [Samaras 72 (Vennegoor of Hesselink 119)], Caldwell, S. Brown, Nakamura; McGeady, McDonald
UNUSED SUBS M. Brown, Crosas
RANGERS McGregor; Whittaker, Broadfoot, Weir, Papac; Davis, Mendes, Ferguson, McCulloch [Dailly 81]; Lafferty [Boyd 75], Miller [Novo 58]
UNUSED SUBS Edu, Alexander
REFEREE Dougie McDonald