Four-time champion John Higgins had led 4-0 against Ali Carter on Sunday, only for the Englishman to win five frames in a row to hold the overnight lead.
Higgins, 50, made breaks of 63 and 81 to go ahead, before Carter’s 106 in frame 12 made it 6-6, although the Scot won four of the next five frames to advance 10-7.
That sets up a last-16 match against either seven-time champion Ronnie O’Sullivan or Chinese debutant He Guoqiang.
“That’s the first time here I’ve been 4-0 up and then gone 5-4 behind so it was not a great sleep,” said Higgins. “But I tried to forget about that and get on with my game.
“There’s nobody that has more respect for Ali as a snooker player than me, I’ve played him so many times and sometimes he has been cueing like a dream.
“Deep down when my name was pulled out against him I was not happy – you know you’re in for a mammoth game so I’m over the moon I got the win.”
Carter, beaten by O’Sullivan in the 2008 and 2012 finals, has now gone out in the first round in the Crucible in four years in a row.
“I made a couple of mistakes and got punished severely, just a little bit of a run of the balls – I’m as sick as a dog,” said Carter.
Ding Junhui, the 2016 runner-up, completed a 10-5 win over David Gilbert, having held a 7-2 lead following Sunday’s opening session.
In an all-Chinese last-16 tie, Ding will take on Zhao Xintong, who became the country’s first world champion in 2025.
China’s 10th seed Wu Yize made one century and five half-centuries in a one-sided session to lead compatriot Lei Peifan 8-1.