The world number 91 lost in qualifying and was only handed a place in the main draw after compatriot Kei Nishikori's late withdrawal with a wrist injury.
But despite blowing three match points when serving for the match at 6-5 in the third set, Sugita regained his composure to edge a final set tie-break to make the third round.
Dominic Thiem is safely into the last 16 as the third highest seed left in the draw brushed aside Britain's Kyle Edmund 6-1, 6-4.
Australia's Bernard Tomic will be Andy Murray's opponent when the world number one gets his tournament underway on Wednesday after seeing off big-serving German Dustin Brown 7-5, 4-6, 6-2.
Another German had a better day though as 20-year-old eighth seed Alexander Zverev saw off clay court specialist Nicolas Almagro 7-6 (7/4), 4-6, 6-4.
Rafael Nadal also begins his quest for a 10th title in Barcelona on Wednesday against Renzo Olivo or Rogerio Dutra Silva.