The two Welsh sides met for the first time in the top flight and Steven Caulker's headed goal was enough to earn Cardiff all three points over their fierce rivals.
It was Bellamy who set up the goal from a corner kick and the lifelong Blues fan has admitted that it was an important victory for his side.
"I'm 34 now so I will celebrate any goal. It was a derby win but a big three points for us, next month we have some really tough fixtures," BBC Sport quotes him as saying.
"I've played in other derbies; Manchester, Liverpool and Glasgow and [the other non-Welsh players] get a sense of what it means to the team and the supporters."
Cardiff are now 12th in the Premier League table and have moved one position above Swansea after their win.