Charlton had already been reduced to 10 men before Jonjo Shelvey fired them into a 38th minute lead after drilling home from Akpo Sodje's pass.
Sam Sodje was sent off for a two-footed challenge on Jon-Paul McGovern in the 18th minute, his second red card in six matches, and things got worse for the home side when Deon Burton followed him in the 41st minute when he received a second yellow card for a deliberate hand ball.
Swindon, who had rarely threatened in the first period, made the most of their two-man advantage and dominated the second half.
Their pressure paid off in the 57th minute when Charlie Austin side-footed the equaliser after a low cross from Kevin Amankwaah.
Austin then turned provider as he hit a low cross from inside the box on the right for Billy Paynter to slot in at the back post in the 74th minute.
However, in the 94th minute, Llera latched on to a long ball from Jose Semedo and coolly placed the ball over David Lucas to level the match in the dying seconds.