Downs looked to put on the early pressure but the Barca defence kept a cool presence in the opening seconds.
The Brazilians were quickly pushed back, though, when a sloppy clearance from Bangaly Soumahoro fell to Ousmane Dembele, who blasted into the top corner on three minutes.
Percy Tau had the best of the opportunities for Sundowns when he went one-on-one with Marc Andre Ter Stegen, but the German made an easy save.
Luis Suarez was proving troublesome and got goal-side to flash a shot on the right narrowly wide a minute later.
The Uruguayan wasn’t to be denied for a second time as he made the next opportunity count with a well-taken finish through the legs of Denis Onyango following a well-executed move on 18 minutes.
Despite trailing and looking well out of reach, the Brazilians continued to put on a never-say-die spirit and their next effort gave a scare to Ter Stegen, who pushed Wayne Arendse’s header onto the post.
Barca went about business casually and nearly made it three after a quick counterattack was picked by Dembele, whose lob over Onyango was hastily cleared off the line by Hlompho Kekana.
The post was the victim once again, as it denied Barca another goal as Denis Suarez headed against the woodwork from Dembele's cross.
After the break, Barca made wholesale changes with Gerard Pique, Sergi Roberto, Paulinho amongst 10 substitutes made after half-time.
They continued controlling the match the way they did in the first half and were inches away from adding more through Paulinho and Pablo Alcacer.
Kekana didn’t let up with his shots from range and gave it another go from but Jasper Cillessen held safely.
The smooth sailing nature continued for Barca, who added a third following a defensive lapse, which Andre Gomes capitalised on to curl past Kennedy Mweene on 66 minutes.
Downs did eventually manage a consolation goal through Sibusiso Vilakazi after a good inside pass from Tau on 75 minutes.
Tebogo Langerman broke free on the left, but despite having a clear chance to score, he opted for a square pass, which was cut out with Tau waiting at the far-post.
In the final stages, Barca’s passing took centre stage as they settled for the win ahead of their final league outing of the season, against Real Sociedad on Sunday.
Sundowns: Onyango, Langerman, Arendse, Soumahoro, Ngcongca, Mabunda, Kekana, Vilakazi, Billiat, Zwane, Tau.
Subs: Mweene, Manyisa, Sirino, Madisha, Zulu, Sekotlong, Brockie, Lebese, Morena, Ngoma, Nascimento.
Barcelona: Ter Stegen, Semedo, Digne, Mina, Rakitic, Busquets, D.Suarez, Alena, Iniesta, L.Suarez, Dembele.
Subs: Cillessen, Piqué, Messi, Coutinho, Paulinho, Paco Alcácer, Jordi Alba, S.Roberto, André Gomes, Aleix Vidal, Galarreta i J.Cuenca.