It sets up the possibility of a second successive Champions League final for The Brazilians, though there will be much work to do in Saturday’s second leg in Pretoria.
Here are the talking points from the game.
Superb goal
The decisive moment in the match came on 51 minutes and was delivered by Colombian Brayan Leon with a close-range header.
It was a superbly constructed goal as Jayden Adams’ long pass to the right flank was volleyed into the six-yard box by Thapelo Morena and Leon was on hand to score, ghosting between two defenders.
He continues to be an excellent signing, scoring his ninth goal since his January arrival, four of which have come in the Champions League. He has made 10 starts (18 appearances in all), so his strike rate is very good.
Chances go begging
Arthur Sales has had a few misses in recent weeks and the Brazilian again found himself in a good shooting area, but waited too long to get his effort away and it was blocked.
He is a superb player but looks a little short on confidence at the moment. If Sundowns can get him firing again they become an altogether different threat.
He has not scored for Sundowns since a Champions League goal against Al-Hilal in January and has just five goals for the season in all competitions, too few for a player of his quality.
Frenchman Florian Danho hit the upright for Esperance with a thumping volley and then later missed a headed chance as the Tunisians showed they remain a dangerous side.
Goal disallowed
Esperance thought they had equalised through Aboubacar Diakite, but the Video Assistant Referee (VAR) spotted a foul on goalkeeper Ronwen Williams that was not initially seen.
There was an elbow in the face of Williams from defender Hamza Jelassi as he went up for the ball along with teammate Sales. The clash saw the ball slip, allowing Onuche Ogbelu to cross for teenage substitute Diakite to head home.
At first, it looked as if Sales had fouled his own keeper, but after being sent to the touchline screen, referee Mustapha Ghorbal agreed that Williams had been fouled, and so Diakite’s effort was ruled out.
Williams should have punched away the cross rather than try to catch it, and it proved a lucky let-off.
Brilliant Mudau
Right-back Khuliso Mudau made two vital first-half interventions, underlining why Esperance wanted to sign him at the start of the season.
Mudau sat out the beginning of the campaign while he tried to force a move away from Sundowns, but in the end had to go back with his tail between his legs as Sundowns stood their ground.
There was also a smart tackle from Grant Kekana, who will hope that Hugo Broos was watching to give him an opportunity to get back into the Bafana Bafana set-up.
But Kekana was later sent off for a high boot, a decision that was a little questionable given a yellow card might have been the better sanction.
Possible final opponents
Should Sundowns complete the job, then it seems likely they will face Moroccans FAR Rabat in the final.
FAR Rabat and newcomers Renaissance Berkane met in a derby clash on Saturday night, with second-half goals from Ahmed Hammoudan and substitute Khalid Ait Ouarkhane seeing the military men win 2-0 in their semi-final first-leg tie.
Hammoudan opened the scoring in the 58th minute before Ait Ouarkhane added a second 10 minutes from time. The return is next Saturday night in Berkane.