UK and Masters champion Selby missed a red at 33-11, with Bond putting in a superb 56 break to take the win.
There were no such worries for Stephen Maguire, who beat Matthew Selt 59-30 as Selt missed a critical long blue.
Defending champion Barry Hawkins cruised through with a 73-1 win over Anthony McGill.
Ben Woollaston missed a red at 33-46 to let Michael White win their clash 82-33.
The draw for the last 16 takes place on Sunday afternoon.
Last 32 results:
Stephen Maguire 59-30 Matthew Selt
Michael White 82-33 Ben Woollaston
Andrew Higginson 45-29 Robert Milkins
Dominic Dale 61-17 Marcus Campbell
Thepchaiya Un-Nooh 42-41 Alan McManus
Dave Harold 61-36 Gerard Greene
Barry Hawkins 73-1 Anthony McGill
Nigel Bond 67-33 Mark Selby
Mark Allen 65-8 Peter Lines
Martin Gould 61-1 Mark Joyce
Liu Chuang 58-18 Ricky Walden
Kurt Maflin 57-16 Mark Davis
Jack Lisowksi 48-41 Robbie Williams
Mark Williams 45-37 Jamie Jones
Jimmy Robertson 67-8 Anthony Hamilton
Michael Holt 40-31 Ryan Day