The hosts went on the attack from the beginning, with Denis Onyango making a great save in the 11th minute to deny them an opener.
Further chances fell to Guillaume Nicaise Daho in the 16th minute and Abdellatif Noussir in the 22nd, but the Sundowns defence survived the first quarter of the game.
However, in the 26th minute, they finally caved in as Salah Eddine Saidi found the back of the net with a header.
Buoyed on by a vociferous home crowd, Wydad continued to put pressure on Sundowns after the goal.
Sundowns, by contrast, were generally restricted to audacious shots from distance — as was also the case in the first half of the first leg.
In the 51st minute, Hlompho Kekana squandered a golden opportunity to regain the aggregate lead as he fired off target from right in front of goal.
The game slowed down after that and Sundowns’ frustration began to show, particularly when Motjeka Madisha was booked for a pull-back.
Pitso Mosimane looked to change it by bringing on first leg goalscorer Yannick Zakri for Khama Billiat in the 73rd minute.
Mosimane made his other substitutions in the 82nd and 88th minute respectively, as George Lebese and Bangaly Soumahoro came on for Themba Zwane and Wayne Arendse, who had picked up a booking moments earlier.
Percy Tau almost found himself through on goal in stoppage time, but Amine Atouchi took one for the team, bringing him down. He was fortunate to escape with only a yellow.
After 180 minutes, nothing could separate the sides on aggregate and they went to penalties.
Sundowns drew first blood in the shootout as Onyango saved Atouchi’s penalty.
However, their advantage was cancelled out when Tau missed his spot-kick.
The next player to fail to score was Zakri, who had a poor penalty saved, gifting Wydad the upper hand.
Then, Soumahoro skied his penalty and it was all over. The defending champions had crashed out of the tournament, but not without an almighty fight in a classic CAF Champions League quarter-final.
Sundowns: Onyango, Langerman, Arendse (Soumahoro, 88’), Madisha, Mabunda, Kekana, Manyisa, Zwane (Lebese, 82’), Morena, Tau, Billiat (Zakri, 73’).