A tournament-high 142 helped Hawkins take a 3-1 lead, but Higgins hit back with two centuries of his own (107 and 138) to trail 4-3.
Hawkins then moved within a frame of victory, only for Higgins to win the next two and take it to an 11th and final frame.
And it went right down to the wire, with Hawkins sinking all six colours after a safety exchange to win the decider 66-60 and book a last-eight meeting with Neil Robertson.
O'Sullivan lifts Shanghai title for third successive year
15/09/2019 AT 14:24
A strong start from Robertson helped the Australian overcome Ding Junhui to reach the last eight.
Robertson, the 2010 world champion, raced to a 4-0 lead with breaks of 72, 82, 101 and 69.
Ding fought back, but the two-time winner in Shanghai could not turn the match around, losing 6-3 as Robertson posted 71 in the ninth and final frame.
Robertson will face the winner of the final round-two match between John Higgins and Barry Hawkins.
Meanwhile, reigning world champion Judd Trump advanced to the last eight with a 6-4 victory over David Gilbert.
'That is an outrageous fluke!' - Trump benefits from slice of luck on way to century
Trump lost the first frame before reeling off four frames in a row, and though breaks of 111 and 86 helped Gilbert reduce the deficit, world No 1 Trump hit a century of his own to close out the match.
Mark Allen will face Trump in the quarters after the seventh seed edged past Liang Wenbo 6-5.
Wenbo opened with a 130 break before going 3-1 up, only for Allen to lead 4-3 and then lose the next two frames.
Trump produces delightful double against Gilbert
Allen held his nerve though, as a break of 72 helped him level before he won the decider 88-38.
The last-eight matches will take place on Thursday, with defending champion Ronnie O’Sullivan already through to play Kyren Wilson, while Shaun Murphy is up against Jack Lisowski.
Thursday’s quarter-final matches
- Ronnie O'Sullivan  v Kyren Wilson 
- Barry Hawkins  v Neil Robertson 
- Shaun Murphy  v Jack Lisowski 
- Mark Allen  v Judd Trump 
O’Sullivan wins third consecutive Shanghai Masters
15/09/2019 AT 09:06
O'Sullivan knocks in second ton against Murphy
15/09/2019 AT 14:14