The Welshman, who lost a 6-2 lead, found another gear when tied at 7- 7 to run out a 10-7 winner. The 1998 UK Championship runner-up next plays Malta's Tony Drago for a place in the quarter-finals.
Stevens fluked the penultimate red in frame 16 to clear up with 39 and then sank a brilliant final brown from distance with the white tight on the baulk cushion to clinch victory.
Ken Doherty came close to joining The Crucible's "maximum-break club" yesterday, the former world champion taking blacks with the first 13 reds during frame 12 of his opening-round game against Steve James. The Irishman reached 104, but with a pounds 147,000 prize beckoning Doherty lost his position on the penultimate red. He tried to keep the break going by doubling the ball into a middle pocket but had to settle for setting up a second-round match with Nigel Bond, winning 10-3.
"The main thing was to win the match but it was a great chance," admitted Doherty, the world champion in 1997 and runner-up last year.
Doherty also made runs of 57, 81, 56, 54 and 65 while James gained one of his three frame successes with a 137 clearance.
Another seed to lose yesterday was Canada's Alain Robidoux when he was beaten 10-6 by England's Nick Walker.
Walker admitted he was affected by the unique Crucible atmosphere. "When I broke off I just told myself 'please don't hit the blue'. I was so nervous in the first frame I couldn't see the balls. Even if Alain had left them over the pockets I doubt whether I would have knocked them in. And then when I got to the interval I told my manager I didn't want to go out there."
Walker calmed down and the breakthrough came when he snatched frame 15 to lead 9-6 and then recovered from 49-7 down to take frame 16, clearing the last two reds to pink for a match-clinching 31 break.
In an encounter between two far-eastern competitors, Thailand's James Wattana established a 5-4 overnight lead over Marco Fu, the 21-year-old from Hong Kong.
EMBASSY WORLD CHAMPIONSHIP (Sheffield) Today's games: Morning session (10.00): M Williams (Wal) v I McCulloch (Eng); J Wattana (Thai) v M Fu (HK). Afternoon session (14.30): M King (Eng) v D Morgan (Wal); S Davis (Eng) v J Perry (Eng). Evening session (19.00): Williams v McCulloch; S Hendry (Sco) v P Hunter (Eng).Reuse content