Chiefs looked to be crashing out of the competition they won last term as they were 2-0 down at half-time against the Team of Choice at FNB Stadium.
However, the hosts returned with vigour after the interval to dispatch Komphela's former employers in his first assignment as Amakhosi boss.
Man of the Match George Lebese hit a brace either side of a Bernard Parker goal, while debutant Siyanda Xulu made amends for an own goal with a stunning strike in extra time before Hendrick Ekstein secured the result at the death.
Komphela said: “In the dressing room all that we said is, 'listen, adversity is the breakfast of champions. If we are going to defend this trophy then we need to come out of this have to start better in the second half,' which we did."
The former Bafana Bafana defender felt it was crucial to show support to Xulu after he headed past his own goalkeeper Reyaad Pieterse late in regulation time.
"When the player makes an error, like Xulu, ignore it. Keep on the positive and support him."
Komphela, though, is naturally hopeful his charges tighten up at the back in future.
"I'd like to see a Kaizer Chiefs team that is stingy with conceding goals."
Bloemfontein Celtic, Bidvest Wits and Ajax Cape Town are also through to the last-four, with the PSL set to decide the two-legged match ups via a draw on Thursday.