Gary Wilson will be met by Ronnie O'Sullivan on his Crucible debut.
He admits the last frame "turned into a war" and that his concentration was shot, "if you'd asked me to count to ten I would've got to five and nodded off", but he persevered as a "chess match" ensued between the pair, which included a rare mid-frame toilet break, such was its staggering longevity.
'You hear so many players using the excuse "I was mentally shattered, I couldn't carry on" and that's why it should always be the biggest test because it tests every facet of your game, your temperament, your stamina, your skill and ability to cope with pressure'.
Scotland's Dott was also involved in a right tussle as he won the last three frames to overcome Jamie Jones 10-8.
Wilson reached the final round of qualifying after claiming a 10-7 over Peter Lines before thrashing White, a former World quarter-finalist, to book his place in the first round draw.
And world number 51 Grace said: "Being a big guy, I might be banging into the furniture".
"I'm looking forward to the draw now". "A two table set-up and old guys sitting round in chairs!"
"I have been to watch and you feel you can reach out and touch the players in the first two rows".
And with this year's World Championships starting on Saturday, the 48-year-old looked back at some of his most memorable moments.
The 31-year-old has won the women's World Championship an unprecedented 11 times but was unable to haul her way back into contention having trailed Walker 6-2 overnight; eventually succumbing in the evening session.
Chinese star Ding Junhui, seeded fourth, has been paired with compatriot and fellow Sheffield-based player Zhou Yuelong, who is making his Crucible bow.
Chinese cueman Ding Junhui may not have had a great season but the whole of China and many neutral observers will be willing him to go one better than previous year and become Asia's first world champion.
"We haven't played a single pro match but he's been on the radar in the qualifiers for a long time".
The 17-day tournament runs through to May 1, and the champion will collect record prize money of £375,000.