The veteran goalkeeper, who turned 43 on Saturday, came on for the final five minutes of his side's 4-1 thumping of Japan in Cuiaba on Tuesday.
Mondragon, due to retire after the tournament, was brought on to replace David Ospina in a sentimental gesture by Pekerman, and was called into action at the very end of the game, rushing from his line to deny Yoichiro Kakitani.
After breaking the record previously held by Cameroon's Roger Milla, who was 42 at the 1994 finals in the United States, Mondragon revealed it was because of Pekerman that he had prolonged his career.
"Jose Pekerman convinced me to continue playing," he said. "I will never forget that.
"If it wasn't for him, I would have retired two years ago.
"I feel privileged to be here, it was my best birthday ever."
Jackson Martinez, who scored twice in the second half as Colombia ended their Group C campaign with a 100 per cent record, was delighted he was able to contribute to a winning effort.
"I'm very, very happy for this great blessing," he said.
"All of Colombia is supporting so that things go better."
