Tashreeq Matthews opened the scoring in the Second Preliminary round first-leg qualifier at M.K.O. Abiola International Stadium after 12 minutes.
Peter Shalulile added a second with four first half minutes remaining before Miguel Reisinho netted his first goal for his new team with 61 minutes on the clock.
Substitutes Arthur Sales (74') and Katlego Ntsabeleng (84') both scored shortly after they were introduced, as Samson Olasupo (76') netted a second-half consolation.
The result gives Sundowns a massive advantage heading into next week's second leg.
Speaking after the encounter, Cardoso explained that Sundowns spent a lot of time researching their opponents.
He said in the Citizen: "We saw six matches from Remo Stars. Not only from the two qualifying matches from the previous round of the Champions League but we also saw four matches from their championship.
"I even went as far back as last year for their game they played against AS FAR. That's how much we studied them and that's also the commitment you need to have when you play these kinds of matches by going deep when studying your opponent.
"If you don't study a team like this, you will be surprised."
Cardoso added: "It's not easy to play against a team that has a lot of man-to-man marking all over the pitch.
"I think the players understood very well the work we put in since we gathered to prepare for this match.
"It was a matter of keeping a good attitude because to score 5 goals against a team that are champions of Nigeria is not easy."
Orlando Pirates head coach Abdeslam Ouaddou has challenged his players to believe they can end the club's 31-year wait for a second CAF Champions League title after securing their place in the group stages.
Mamelodi Sundowns coach Miguel Cardoso has admitted that his team's mistakes and failure to manage their emotions proved costly as they suffered a shock elimination from the CAF Champions League.
Orlando Pirates breezed into the CAF Champions League group stage after a dominant 4-0 victory over Namibian side African Stars at the Orlando Stadium to secure a 5-0 aggregate victory.
Mamelodi Sundowns have been eliminated from the CAF Champions League by Angolan Girabola league leaders Wiliete SC on away goals.
