Kermit Erasmus put the hosts in front early in the cup clash as he found the back of the net in the 24th minute, and the Bucs enjoyed the lead until half-time.
However, Venda were not about to roll over for the Soweto giants and fought back to level matters four minutes into the second half thanks to a strike from Edmore Chirambadare.
Pirates failed to find a winner before the end of 90 minutes and the game entered extra-time.
Thembinkosi Lorch stepped up for the home team in the 113th minute to score the decisive goal and book their place in the last eight of the cup.
Golden Arrows 1-3 Royal AM
Over at the Sugar Ray Xulu Stadium, Royal AM knocked Golden Arrows out of the tournament thanks to two extra-time goals.
A Ricardo Nascimento penalty in the 33rd minute put the away side in the lead, and they seemed destined to grab the win in regulation time, but Arrows netted a stoppage-time equaliser.
It was Knox Mutizwa complicated matters for Royal as he bagged the leveller for the hosts in the fourth minute of stoppage-time.
Despite the momentum shift it was Royal who came out on top in extra-time. Levy Mashiane scored in the 110th minute before completing his brace in the 119th minute to secure safe passage for Royal AM.
Chippa United 2-0 Mpheni Home Defenders
It was a more straight-forward affair at Sisa Dukashe Stadium where Chippa United secured a comfortable win over Mpheni Home Defenders.
Ronald Pfumbidzai put the Chilli Boys in front in the 31st minute and it was Diego Appollis who capped off the win in the 70th minute to send the home team through to the quarter-finals.