Skevofilakas was born in 1940 in the Athens suburb of Nea Ionia. He started his career at Eleftheroupolis where he was discovered by Tryfon Tzanetis, joining AEK in 1960. His career at AEK lasted 13 years. Afterwards, he joined Atromitos Athens.
Skevofilakas was capped 15 times by the National Football Team of Greece.