Amakhosi, who were recently beaten 1-0 by Black Leopards, prevailed through efforts from Lehlohonolo Majoro and Abia Nale, while Patrick Malokase netted for Dikwena at the Royal Bafokeng Stadium.
"It was important that we bounce back following our defeat against Black Leopards on Tuesday," Vermezovic told Chiefs' website.
"We played against a team that has improved a lot in the past couple of weeks and it is a massive victory for us and credit should go to the players for doing well out there.
"It is never easy to come here and win and we are delighted with the three points."
The Serbian admits, however, he is struggling to inspire consistency in his charges, who trail leaders Orlando Pirates by six points but with a game in hand.
"It is very difficult to understand why we do not seem to apply ourselves consistently in each and every game," said Vermezovic.
"We prepare for all games the same and I feel we need to be more consistent. This is something that I am addressing with the players."
The Glamour Boys next face Free State Stars in the Nedbank Cup quarter-finals on Saturday.