The world number 523, who reached the second round of the main draw back in 2008, overcame Benjamin Mitchell of Australia 7-6 (7-4) 4-6 6-3 despite being ranked 287 places below his opponent.
Edmund also progressed in three sets following a 6-3 6-7 (4/7) 6-4 victory over Daniel Gimeno-Traver of Spain.
However it was not such a good day for the other Brits in action as Andrew Fitzpatrick, Edward Corrie, George Morgan, David Rice, Richard Bloomfield and Liam Broady all crashed out.
Corrie was defeated 6-4 6-3 by France's Stephane Robert while Morgan suffered a crushing 6-0 6-4 defeat at the hands of Spaniard Inigo Cervantes.
Fitzpatrick fell 6-3 6-4 to Marco Chiudinelli although Rice put up a slightly better fight as he lost 6-3 4-6 6-2 against China's Ze Zhang.
Bloomfield was beaten 6-4 6-4 by Japan's Hiroki Moriya before Broady saw a 5-2 lead in the opening set quickly disappear in a 7-6 (7/5) 6-4 defeat to Thomas Fabbiano.