According to the Football411 website, After 90 minutes without a goal, Bernard Parker's well-struck effort four minutes into extra-time was enough to secure victory for Amkhosi at the Moses Mabhida Stadium.
The weekend's cup triumph capped off an incredible season for the Glamour Boys, who last week lifted their first Premiership trophy since 2005.
GALLERY: Chiefs win Nedbank Cup
For Baxter, who was appointed head coach at Naturena ahead of the 2012/13 campaign, it has been a dream first season at the helm of the Soweto giants.
"I'm immensely proud of my players after this season, and just immensely proud of what they were able to achieve in a cup final," the Englishman said in his post-match interview.
"If someone had told me at the start of the season we would win the double I'd ask them what how much they were drinking?
"But as the season progressed, we all started to believe (we could do it)."
He added: "The first half (on Saturday) was a bit so-so, but then the game opened up and we found pockets of play behind them to exploit.
"We then spread the ball around and used the field beautifully with controlled play... and I'm just absolutely delighted."
Baxter's success this past season with Chiefs could see him scoop the PSL's Coach of the Season award, with the former South Africa chief vying with Platinum Stars' Cavin Johnson and Bloemfontein Celtic's Clinton Larsen for the accolade at the end-of-season ceremony to be held on Sunday.