First-half goals from Michael Majoro and Josta Dladla sealed the tie with former Dube Birds defender Keegan Ritchie named as Man of the Match.
After getting their season off to a 2-1 win over Jomo Cosmos, Vlad V said that his side had put in a stronger performance.
He said after the game: "I think it was a better game than our last one."
The Serbian felt his side might, however, failed to capitalise on a number of chances created in the first half and go on to rue their misses.
"We have lifted our form from game to game and especially in the first half we could have scored more goals."
"But I was afraid because the rule in sport is if you miss chances, you can lose the game.
"But in the second half we kept the ball much better and they started to play with the long ball."
Vermezovic decided to rest a number of players with a MTN8 semi-final against Ajax Cape Town only days away and in the second half he withdrew influential midfielder Siphiwe Tshabalala as well as Lehlohonolo Majoro while Bernard Parker only came on in the second period.
"I tried to save our players because in three days we have another important game", he concluded.
Swallows boss Gordon Igesund was naturally disappointed with his side, especially their first half performance.
He said: "I was disappointed with the first half as we were not in the game at all.
"They had quite a few chances and lost our shape completely. We didn't play near our capabilities. We need to be tougher in the middle of the park."
Igesund congratulated his opponent but conceded he though their opening goal, scored by Majoro could have been offside.
"Well done to Kaizer Chiefs, they played really well today.
"Their one goal looked suspect, it looked offside, but regardless they looked the better team and deserved their victory.
"We will take each game as it comes and pick ourselves up."
Ritchie was handed a cheque for an impressive performance for Amakhosi and revealed his delight at having settled in to his new surroundings.
"It was a good game, it's always nice getting against your former team.
"I came here to work hard and that's what I did.
"I am settling in quite well. The guys are getting to know me a bit better. Guys like Shabba and Josta are understanding my game a bit better.
Ritchie came close to scoring against Swallows and admitted it 'was unlucky' not to have found the net.