Local boy Alejandro Falla delighted the home fans by upsetting eighth seed Malisse 6-1 3-6 6-1 to book his place in the second round, where he will face Matthew Ebden of Australia.
And it was another Australian, James Duckworth, who accounted for seventh seed Bedene, claiming a 6-3 6-4 win.
Ivo Karlovic claimed a 7-6 (7/5) 6-4 win over Juan Ignacio Londero to book a meeting with third seed Igor Sijsling,
Ruben Bemelmans overcame Colombian wildcard Nicolas Barrientos 7-5 6-3, while Emilio Gomez saw off another home hope, Eduardo Struvay 6-4 6-4.
There were also wins for Vasek Pospisil, Chris Guccione and Victor Estrella Burgos.