The Brazilians won the first leg in Tshwane 1-0, but a 3-1 defeat in Lubumbashi meant there would be no extended African campaign for Pitso Mosimane’s men.
Teko Modise and Mzikayise Mashaba were the only changes to the side that won the first leg.
Denis Onyango was called upon to make a clearance as early as the seventh minute, and three minutes later Ramahlwe Mphahlele needed to be alert to clear the danger.
Mazembe had the ball in the back of the net in the 28th minute, only for it to be ruled offside.
But the goals did eventually come, with Rainford Kalaba getting the opener on 36 minutes.
Mazembe got their second on the stroke of halftime, with Mbwana Samatta netting on this occasion.
This left Sundowns with a mountain to climb – a mountain which went from Kilimanjaro to Everest on 57 minutes when Roger Assale netted a third.
To their credit, Sundowns did not give up and the introduction of Mame Niang on 74 minutes really caused headaches for the home defence.
Modise forced the keeper in a diving save with his volley, before Niang headed just wide from Percy Tau’s cross.
Their goal did eventually come on 84 minutes when Tau buried a chance from Niang’s knock-down, but Sundowns just couldn’t get the second goal and crash out of Africa.
Sundowns XI: Onyango, Mphahlele, Schut, S Zwane, Mashaba, Zungu, Kekana (Niang 74), Modise, Billiat, T Zwane (Laffor 53), Malajila (Tau 66)
TP Mazembe XI: Kidiaba, Frimpong, Kimwaki, Coulibaly, Kasusula, Diarra, Adjei, Asante, Assale, Samatta, Kalaba