The controversial Australian's opponent Santiago Giraldo withdrew with injury when Kyrgios led 6-1 2-1.
Seventh seed Kyrgios, who was not selected in Australia's teams for their Davis Cup semi-final loss to Great Britain, will now play either Tatsuma Ito or Jarkko Nieminen in the second round.
The 20-year-old is hoping to end the year on a positive note - and rebuild his reputation - after his now infamous sledge to Stan Wawrinka in Montreal.
He has dropped from career-high world ranking of 25 in June to 41st.
Kyrgios' compatriot Sam Groth who was beaten 6-1 7-6 (8-6) by Benjamin Becker.