Hawkins will meet another two-time champion, Neil Robertson, in the last eight after the Australian edged Welshman Jones 4-3.
Jones had made a flying start with a 126 break, before Robertson responded in kind with a 122 break.
With the match later tied at 3-3, Robertson came out on top of the deciding seventh frame to claim victory.
Jones’ exit left Page as the only Welsh hope, but he was beaten by Jack Lisowski who amassed breaks of 67, 84, 99 and 54 in a convincing 4-2 victory.
Lisowski will be hoping his tournament form continues when he takes on fellow Englishman and 2017 champion Stuart Bingham, who beat Chinese world champion Zhao Xintong 4-2.