Gorowa’s countryman - Nyasha Mushekwi, was in deadly form early on, netting the opening two goals of the match in a four minute period, while Richard Henyekane scored the other.
Tony Tsabedze got the consolation goal for Santos.
Despite the score-line, it was not one-way traffic with Sundowns putting in a professional and accomplished performance.
The tone was set within 40 seconds as Santos keeper Tshepo Motsoenoeng was forced in to making a double save from Matthew Pattison and Mushekwi.
Santos had their first chance in the sixth minute, through the ever-impressive Erwin Isaacs, who took aim for the top corner from 25 yards, Wayne Sandilands tipped the ball to safety.
Mushekwi got his first in the 16th minute with a superb header, doing really well to beat Wayne Arendse to a corner and power the ball beyond Motsonoeng.
Mushekwi doubled his tally just four minutes later, with his eighth League goal, when he ran onto Pattison’s clever through-ball and found the back of the net, using the space between Motsonoeng’s legs to get it there.
Santos refused to give up, however, and Isaacs was only a yard over the bar with a sweetly-struck free-kick.
The Cape side kept on fighting and pulled a goal back in the 31st minute when Vuyisile Wana floated up a cross to the back post, where Tony Tsabedze side-footed home.
The first chance of the second half didn’t take long to arrive as Lebohang Mokoena curled a shot just over from the edge of the box within a minute of the restart.
Santos had the chance to level matters on the hour mark, but after Wana raced clear of the defence he was unable to hit the net, sending a left-footed shot just wide of the far upright.
Overall though it was the Brazilians who looked slightly more dangerous in attack and a third goal always seemed a possibility, while Santos, despite throwing on several attackers, struggled to breach their opponents’ defence.
There was another chance for Mokoena eight minutes from time, but he was unable to curl his left-footed shot inside the far post, going just wide.
Substitute Mabuthi Khenyeza should really have made it 3-1 in the 80th minute.
With Santos pushing for an equaliser, he found himself with plenty of space and time to hit the target, but from 16-yards out right in front of goal he curled the ball wide.
Richard Henyekane netted his first goal in extra time for the club with an easy tap-in after Elias Pelembe’s square ball.