At one stage in Monday’s afternoon session Williams looked as though he could cross the winning line without needing to return in the evening.
That did not materialise but by stretching his lead from 10-7 overnight to an even more commanding 15-10, the 43-year-old Welshman was just three frames away from the winning line.
Higgins made exactly the start to the evening session that he needed, reeling off three frames in 50 minutes.
He made breaks of 131, 67 and 82, each time ruthlessly punishing mistakes from Williams whose once huge lead was down to just two frames at 15-13.
All the momentum was with Higgins, who had won six of the last seven frames, and Williams desperately needed to halt the charging Scot.
The Higgins roll continued as he took the last frame before the interval too, again capitalising on Williams missing a red.
It would rank alongside the great Crucible final comebacks if Higgins could pull it off.
The drama was relentless and after Higgins drew level at 15-15 there was an unexpected shift in momentum.
Williams reeled off two frames in a row, the second with a 100 break, but then missed a pink in the next frame that was match ball.
Higgins cleared with a run of 65, taking the frame, but Williams was not to be denied glory.
He made 69 in the next to leave Higgins needing snookers, but they did not come. It was not his night, but it very nearly was.