The 29-year-old skippered the side after John Terry was left out of the squad against the Bundesliga outfit.
Frank Lampard and Didier Drogba, who have captained the side in the past, were both not involved in the starting line-up either.
It was the first time the Czech goalkeeper had been given the armband for his club in a competitive fixture, after previously leading the side in a friendly against Crystal Palace.
David Luiz and Juan Mata scored the goals for the Blues and Cech had to keep out two shots on target.
He told his personal website: "I take it as a huge reward for my services. It is a big privilege to be the captain of one of the world's best football clubs, especially in the Champions League.
"It could not have come out better. I saved two chances and we won 2-0.
"It was a perfect game with all that it involves."
It was also the first time manager Andre Villas-Boas had taken charge of Chelsea for a Champions League game and they already top Group E after one match.
Valencia and Genk, who drew in their opener, will face the Stamford Bridge club over the next couple of months.
Cech continued: "It was an important start in the competition and I rate this win high because Leverkusen were an unpleasant opposition.
"But we won and kept a clean sheet. It is positive and will certainly boost our confidence ahead of Sunday's clash against Manchester United."