White, six times a Sheffield runner-up, squandered an 8-4 lead against the 25-year-old world No 22 from Nottingham. It was only the third first- round defeat for the 34-year-old since making his Crucible debut in 1981. He must now qualify for next year's final stages after losing his place in the top 16.
Hamilton made breaks of 78, 96, 65 and 52 to level at 8-8, and finished the match with a run of 54 in the 19th frame.
John Higgins resorted to desperate measures with his match against compatriot Graham Horne in danger of ending in disaster. He called on a cue doctor and referee, Lawrie Annandale, to make emergency repairs during the opening session. Annandale's expertise with a carpentry saw, shortening the cue did the trick as the world No 2 then turned a 3-1 interval deficit into a 10-6 victory.
"Lawrie did a great job as usual because I immediately went out and knocked in a century," the Scot said. That turned the match his way.
Alain Robidoux won his first match at the Crucible since 1992 to qualify for the second round, the French-Canadian beating Brian Morgan 10-8. Morgan, the world No 49, wiped out his 5-3 overnight deficit to level at 7-7 before going ahead for the first time in the match at 8-7 thanks to a break of 72. Robidoux punished an error with a break of 58 to get on level terms and then took the next two frames.