Ba stretched to volley the only goal from Juan Mata's chipped pass before Cech brilliantly saved Javier Hernandez's diving header from point-blank range.
Cech told ITV Sport: "It was a great ball from the wing and Javier did well to direct the ball into the goal. I went fast as I could and left my left arm to do the job. I tried to cover as much space as I could and luckily I was able to reach it."
Ba said of his goal: "It was a brilliant pass from Juan as well.
"For Newcastle I scored quite a similar goal against Man United - it reminded me of that."
The win continues Chelsea's excellent record in the competition, having lifted the trophy in four of the last six seasons.
And Cech said: "It was a great win. We know there is only one way to win the cup and we won the game in a very good fashion.
"We love the stadium (Wembley) and we respect the FA Cup as a whole - that's why we always do well."