The victory brought Chelsea the fourth trophy of Mourinho's reign.
The match also had a sour ending with an ugly brawl breaking out in injury time which saw both managers take to the field of play and Arsenal's Kolo Toure and Emmanuel Adebayor and Chelsea's John Obi Mikel sent off.
"I think we showed character," Chelsea manager Jose Mourinho said after the match.
"Arsenal played a very good game, in my opinion. They showed the reason why they arrived at this game. They beat Liverpool, Everton and Tottenham with this team.
"But the second-half was completely different, we dominated the game and at the end of the day I think we deserved the victory. The pity was what happened in the final (moments). I don't know what happened but it was not nice, especially for them (Arsenal)," Mourinho said.
Wenger stuck to his youthful policy for the League Cup and left the likes of Thierry Henry, Tomas Rosicky or Gilberto Silva out of the side.
Despite their youth, nearly all are still household names and they showed why many have already collected international caps in the opening minutes as they took the game to Chelsea and it was no surprise when Walcott put Arsenal ahead from a corner.
|Tempers flare as the handbags come out |
When Cesc Fabregas's delivery was only half-cleared by Drogba, Abou Diaby slipped a pass through to Walcott and the teenager kept his composure to lift a curling shot over Cech from 12 yards for his first ever Arsenal goal.
Chelsea had hardly mounted an attack at that stage, but the shock of falling behind sparked them into life and within eight minutes they were level.
Michael Ballack's pass picked out Drogba on the right edge of Arsenal's penalty area and the Ivory Coast striker, given the benefit of a tight offside call, ran through to beat Manuel Almunia for his 27th goal of the season.
But with 30 minutes remaining, Chelsea's ambition of collecting more silverware this season took a severe blow when inspirational captain John Terry took a nasty kick in the face from Arsenal's Diaby as he attempted to head the ball goalwards.
The England defender's Terry neck was put in a brace as he was taken from the field at the Millennium Stadium with an oxygen mask fitted.
The Chelsea team doctor added later that Terry had no recollection of events since breakfast on Sunday.
Terry had only been declared fit to play against Arsenal after making a quicker than expected recovery from an ankle injury he had suffered against Porto in Wednesday's Champions League draw.
As the clock wound down Arsenal's youngsters looked increasingly weary and Chelsea, sensing their chance to go for the kill, pushed forward.
The goal they had been threatening arrived in the 83rd minute when Arjen Robben swung in a cross and Drogba got in front of Philippe Senderos to bury a glancing header past Almunia.
Drogba's goal raised the temperature as Arsenal saw their trophy dreams fading and, with just moments left, Mikel and Toure were involved in a shoving match that sparked a mass brawl.
Mourinho and Wenger both ran onto the pitch to try and restrain their players, but Mikel, Toure and his Arsenal team-mate Adebayaor were all sent off by referee Howard Webb.
Adebayor was so furious with the decision that he had to led off the pitch by Arsenal physio Gary Lewin in an extraordinary end to a dramatic match.