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Wiliete won the final round qualifier for the group stage on away goals after a goalless first leg in Angola last weekend.
Sundowns are the first defending African champions not to reach the mini-league phase since TP Mazembe from the Democratic Republic of Congo in 2016.
The Pretoria outfit won the Champions League for the first time in 2016 and repeated the feat last season, edging FAR Rabat of Morocco 2-1 overall in a two-leg final.
Tashreeq Matthews fired Sundowns into the lead after just 11 minutes at the Loftus Versfeld stadium Sundowns share with rugby club the Bulls.
However, Sundowns gifted Wiliete a 49th-minute equaliser when a weak back pass was intercepted by Angolan captain Mabululu and he raced through to equalise with a well-placed shot.
It was the fourth goal of the African campaign for Mabululu, making him the provisional leading scorer this season.
Elimination ends a run of 10 consecutive qualifications for the group stage by Sundowns since beating Zamalek of Egypt in the 2016 final.
While Sundowns are regular campaigners in the premier African club competition, Wiliete are making only their second appearance after losing in the first qualifying round last season.
They overcame Foresters of the Seychelles 5-0 on aggregate to secure a showdown with Sundowns, who had a first round bye.
Victory for Wiliete completed a triumphant night for Angola as Petro Luanda overcame a two-goal first-leg deficit to also book a group place.
Two-time Champions League semi-finalists Petro beat African debutants Scottland of Zimbabwe 3-0 in Luanda to qualify 3-2 on aggregate.
Goals from Ruben Aderito in the first half and Jorge Pereira midway through the second half levelled the aggregate score and Pedro Aparicio won the tie with an 85th-minute strike.
The triumph marked a dream return by Portuguese coach Alexandre Santos for a second spell in charge of Petro. Compatriot Joao Pedro Sousa was fired after the first leg loss in Harare.
Former champions Mouloudia Alger of Algeria also qualified 3-2 on aggregate. They overcame a two-goal deficit from the first leg by beating Enugu Rangers 3-0 in Algiers.
All the Mouloudia goals came in the second half. Chahreddine Boukholda and Mohamed Bangoura netting before Soufiane Bayazid struck in added time to win the tie.