His unbeaten 161 in over six hours at the crease was the highlight of a determined Black Caps effort that tilted the balance of an intriguing match yesterday.
When heavy rain swept across the ground in mid-afternoon, the tourists were poised to build on what was already a challenging target at 314 for six, ahead by 290.
Only 20 more minutes of play was possible on the resumption, with one more wicket being lost for the addition of another 17 runs, before more rain rolled in.
A key factor in his consideration will be that the highest winning fourth innings total in a Test match at the venue is 311 by the Brian Lara-led West Indies against Australia in 1999.
Also Read
Williamson's innings was a masterful effort of concentration and shot-making.
The elegant right-hander stroked 22 boundaries in a classy innings, putting the seal on an outstanding series for the 23-year-old that has brought him 413 runs so far.
McCullum contributed to his team's improved second innings effort, scoring 25 in a 67-run fourth-wicket partnership with Williamson before he fell lbw to Kemar Roach in the fourth over of the day.