Daniel Wells took the scalp of Hawkins, winning by the same scoreline as Jones to book his place in the second round.
Defending champion Mark Allen - who beat Neil Robertson in last year's final - had fewer issues as he dispatched England's Sam Craigie 6-1, with the Northern Irishman boasting the highest break of 141 and making two others over 50.
Allen now faces Mark Davis in the second round, after the veteran Welshman beat Matthew Selt 6-3 on Sunday.
Mark Selby overcame Liam Highfield 6-3, while in the evening session, world champion Judd Trump looked at ease as he triumphed 6-2 over home favourite Zhang Anda.
Trump would have won by a more comfortable scoreline had he potted a final black in the seventh game, but Anda's second frame only delayed the inevitable.
Trump responded with a break of 102 to add to his other century and three breaks of more than 50 to book a second-round clash with Scott Donaldson.