Ursenbacher won the first frame with a break of 54 before the 2013 finalist Hawkins took ten of the next 11 to seal a comfortable progression.
World Championship
'I need to be patient' - McGill on defeat to Bingham at Crucible
28/04/2021 AT 19:30
Hawkins did not register a single century en route to victory, but nevertheless he won the contest with seven half-centuries – comprising runs of 70, 56, 57, 62, 65, 84 and 53 - to see off his Swiss opponent.
The 41-year-old, who was playing with a new cue, will face Neil Robertson in the second round.
Elsewhere, four-time champion John Higgins trails Kurt Maflin 5-3 after the first session of their second-round match.
Higgins constructed runs of 53, 69 and 101 but it was Maflin, who knocked out David Gilbert in round one, who takes the advantage into the second session, due to start 10:00 on Thursday.
Maflin, 36, put together runs of 55, 79 and 81 to lead the The Wizard of Wishaw.
World Championship
'Just can't wait' - Emotional Bingham on reaching semi-finals
28/04/2021 AT 19:28
World Championship
'Brilliant pot' - Trump sinks outrageous long red from cushion
28/04/2021 AT 19:25