The Shanghai Masters champion was 5-4 ahead leading into the day’s play but fell behind 8-7.
Kyren Wilson moves inside world's top 16 after reaching Crucible quarter-finals
However, the 24-year-old from Kettering moved into a 9-8 lead only to surrender the penultimate frame, which lasted 57 minutes, following a comedy of errors on the blue ball.
He composed himself however and ended up winning the decider to clinch a thrilling match 10-9.
Wilson, who picked up two centuries on his way to the win, told the BBC afterwards: "It was a fantastic match and the way snooker should be played. Fans love a decider,
"I come to tournaments believing I can win but try not to get too far ahead of myself."
Wilson 10-9 Perry
72-25 (72), 0-129 (129), 99-0, 13-73 (60), 77-0 (59), 80-0 (80), 53-73 (58), 30-83 (62), 73-59, 35-77
Joe Perry was stunned by Kyren Wilson finding a purple patch of form to grab a 5-4 lead over Joe Perry in their World Championship first round match.
Perry won three of the opening four frames, recording breaks of 87, 63 and 80 as he did so.
Wilson's 130 in frame three showed that he had brought some form to the Crucible, however, and he showed it off after the mid-session interval with breaks of 58, 89 and 61 to close out the evening's play on a high.
WIlson 5-4 Perry
Frame scores: 87-0 (87), 67-60 (63), 0-130 (130), 80-13 (80), 24-83, 118-0 (54, 64), 45-73 (58), 5-89 (89), 1-75 (61)
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