Grant Kekana opened the scoring in the top-of-the-table Betway Premiership clash on 13 minutes.
Lucas Costa added a second with 27 minutes on the clock. Deon Hotto pulled a goal back for Pirates with 57 minutes played, but Costa restored the Brazilians' advantage just two minutes later, as Teboho Mokoena sealed the result with his goal with 12 minutes of the match remaining.
The result saw Sundowns end the afternoon nine points clear of second-placed Bucs at the top of the standings, although having played a game more.
Reflecting on the game, Cardoso emphasised that there is still a long way to go for his team to retain their top-flight crown this season.
He said in the Citizen: "It's important to win, not for a statement win but most importantly, to believe in ourselves more and more. The statement will be in the end when we win the championship.
"Until then, it's just about respect for ourselves. If you don't put your foot on the ground. I love that expression when you say 'hit the ground running' but my feet are on the ground."
Cardoso added: "I know my responsibility and will not let anyone around me not to take things seriously. I will not allow that so let's hope we can keep them (feet on the ground) there but now it's time to cheer up," he added.
"We should be happy with the victory because it's an important victory and we should celebrate when we win but, I told the players 'celebrate today but please sleep well and don't lose time and go out to lose your time' because they need to sleep and recover."