In the opening frame of the second session, Williams drew level with a 90 break, but, White - much like Williams, renowned for his potting - ground out the next to re-take the advantage.
Breaks of 65 and 72 from White gave the young Welshman an 8-5 advantage but he tensed up after the mid-session interval as Williams drew on his ample experience to cut the arrears by taking the 14th frame 54-38.
Williams appeared bereft of confidence and, White, on his first appearance at the Crucible, then made a 90 and followed that with a 96 to secure a place in the next round and consign the two-time world champion to the ignominy of a first-round defeat.
White will face either Stephen Maguire or Dechawat Poomjaeng in the next round.
White had won the final frame of the session to lead Mark Williams 5-4 in their first round match at the Crucible.
The youngster made a highly impressive start to the evening session between the two Welshmen, with breaks of 87 and 55 earning him a two-frame advantage.
The ‘Welsh Wonder’ made a 61 in the third to halve the arrears but White responded with a 67 to take a 3-1 advantage to the mid-session interval.
The debutant then cleared with a 67 to put his more illustrious counter-part in serious trouble at 4-1 with four frames left to play.
However, Williams drew on all his experience to grind out the next frame 66-25 and then followed that with a break of 71 to trail White 3-4 with two frames to go.
Williams was firmly in the ascendancy and he levelled the scores courtesy of a break of 54 but White held his nerve in the final frame of the session to take an overnight lead of 5-4.