Pitso Mosimane's side played like champions elect in the first half as they cut apart the Pirates defence to take the ascendancy and were two goals up at half-time, and it could have been more.
Leonardo Castro gave the Brazilians the lead in the 19th minute with a beautiful finish after superb interplay between himself, Keagan Dolly and Khama Billiat.
'CBD' were at it again in the 37th minute as Castro fed Dolly outside the box, he played a one-two with Billiat before his shot was parried by Brighton Mhlongo, but the ball fell kindly for Billiat who volleyed in off the left-hand post.
Mpho Makola pulled a goal back for the Buccaneers in the 71st minute, absolutely thundering in a direct free-kick from 35 yards out, in off the underside of the crossbar and giving Denis Onyango no chance.
Sundowns sat back to protect their lead for most of the second half, particularly in the closing stages as they played on the counter, but Eric Tinkler's side could not find another goal despite a late rally.
The result extends Sundowns' lead at the top of the table to nine points while Pirates remain seventh.