But this victory, against the best player in the world, is Swail’s best yet and it means that still no first-time winner at the Crucible has successfully defended the crown.
It was an outcome that looked remote at best when Williams took five consecutive frames yesterday to lead 8-3, and at 11-7 the Welshman still looked certain to progress.
However, then came a sensational run from 31-year-old Swail, who surprised everyone by reaching the semi-finals 12 months ago.
A break of 77 made it 11-8, and then Swail enjoyed a slice of luck as he fluked the last red in the final frame before the mid-session interval to reduce his deficit to two.
Instead of composing Williams and halting Swail’s charge, the break had little effect on the duo’s form and the man from Northern Ireland hit new heights as he knocked in his 140 straight from the restart.
That contribution eclipsed the 139s of John Higgins and Matthew Stevens which had led the race for the £20,000 highest-break prize.
A 58 by Swail then made it 11-11, but Williams edged ahead again when his opponent broke down after six reds and blacks, clearly eyeing a maximum, and the world number one hit a courageous 71 to be one frame away from winning.
As the tension mounted, Swail fought back and dug deep to compile a superb 91 to take the match into a decider.
Williams was first in the balls but scored only 11, and that proved his last contribution as Swail got in to make a 55 which secured a memorable triumph.
Embassy World Championship, Sheffield
2nd rd: (16) J Swail (NIrl) bt (1) M Williams (Wal) 13-12. Frame scores (Swail first): 59-13 60-71 82-46 1-69 23-71 87-0 17-55 34-69 29-67 39-60 1-101 (101 break) 61-3 57-23 56-12 18-74 26-61 92-5 29-75 77-48 66-65 140-0 (140 break) 81-40 55-71 91-0 65-11.
Latest Embassy World Championship, Sheffield
2nd rd: (7) K Doherty (Irl) leads M Judge (Irl) 11-5. Frame scores (Doherty first): 16-52 24-64 82-45 74-35 86-28 69-1 102-28 30-94 65-49 74-0 75-20 51-21 0-54 64-52 102-10 17-58.