The two men and their friend Tebogo Nkosi said they were caught up in a mess that nearly ruined their lives.
"It was a horrible experience. It was like a scene from the movie Jerusalema. Police pointed at us with rifles and ordered us to lie down and searched us," said Mgudlwa.
He said when they saw a tracking company helicopter hovering above them in Boksburg, they joked that the next time they came to Johannesburg they would hire one to avoid traffic.
"We said it would only take us 10 minutes to get to Jozi rather than 2 hours. We laughed, not knowing that we were in trouble," he said.
The fourth man, owner of the alleged stolen VW Jetta 5, Mxolisi Nkosi, appeared in the Johannesburg magistrate's court on stolen car charges.
Mgudlwa said it was a lie that they tried to flee from the police.
"We did not know anything about the car being stolen or linked to criminal activities. What we knew was that our friend (Mxolisi) bought it. To prove that we had nothing to do with the offence, charges against us were withdrawn," he said.
The four men were arrested on the M1 on Friday for allegedly being in possession of a stolen car. They were on their way to the ANC victory party at Luthuli House.
Mgudlwa said he did not blame the police for arresting them because "they were doing their job".
Mahlangu, flanked by his wife Twana, said the arrest had affected his family and would have a negative impact on his career.
"I have a child who is doing Grade 2. What is he going to say when he reads that his father has been arrested."
He said he had just come back from Sweden and was hoping to get a contract with a local team.
"There was something in the pipeline. But after all this, I have doubts," he said.
He said he would talk to his lawyer to see if he could take any action against the police.
The last team Mahlangu played for in South Africa was Platinum Stars.
Mxolisi was released on R5,000 bail.