Higgins hit back from behind to scrape a 9-8 win with breaks of 56 and 24 to seal victory and a last-eight meeting with fellow Scot Stephen Maguire, who rounded off a 9-7 win over Mark Selby with a break of 135.
Higgins said: "It's good to be back and I'm motivated full-stop for the second chapter. I just came here to try to win games and tough games are what you want because you know you'll have to play well to win them.
"It was very tough and Graeme doesn't get the credit he deserves for his game. It's such a tough match to win 9-8 and Graeme will be kicking himself because there were a couple of frames I stole from him."
World champion Neil Robertson held off a fightback by Andrew Higginson to move into the last eight with a 9-5 victory. Higginson hit back from 7-1 down overnight to 7-4 before Robertson recovered his composure. Robertson said: "I played a silly shot when I was 7-0 up last night. I thought it was showtime."
Earlier, Stephen Hendry ground his way into a 5-3 lead after a desperately low-quality first session to his second-round clash with Mark Williams.
The Scot had needed all his fighting spirit to overhaul Jimmy White in round one as the game which made him a seven-time world champion deserted him. And the pattern continued, although two half-centuries provided glimpses of Hendry's best form.
Williams shared the first six frames equally despite not making a break higher than 24, and Hendry's 28 was the highest contribution in a seventh frame which saw him retake the lead.
The Scot then extended his advantage as a 44 set him on his way to victory in frame eight before both players left the arena.
Stuart Bingham carried on where he left off in his win over Ronnie O'Sullivan by surging into a 6-2 lead over Marco Fu.
The world number 23 had runs of 40 and 50 in frame one and 76 in frame three to help him to a 3-1 lead at the interval. When the players returned, Fu narrowed the gap with a 70 before a 56 and a closing 90 saw Bingham re assert his dominance.
Shaun Murphy racked up two century breaks as he took a narrow lead against Ryan Day.
The world number four hit 100 in the opening frame but the four frames before the interval were shared, Day sealing frame four with a 70. Murphy edged back in front after a scrappy fifth frame and a 131, the highlight of the session, saw him open up a two-frame lead for the first time. Day cut the deficit but Murphy wrapped up proceedings with a 78 to take a 5-3 advantage.
Mark Joyce leads Judd Trump by the same scoreline after recording breaks of 62, 87, 100 and 79.The Bristol youngster took two of the first three frames but Joyce, the conqueror of Ali Carter in round one, led 5-2 until Trump took the closing frame.