They are 233-4, with Henry Nicholls not out on 52 and BJ Watling with him on 18.
Williamson brought up the milestone when he ran a quick single after resuming nine runs shy of the mark with New Zealand on 175-3. England's James Anderson catches the ball thrown by team mate Stuart Broad during the second day of the first cricket test match.
After an eventful first day on which England were bowled out for only 58, the first day-night Test match in New Zealand has effectively come to a soggy halt.
Williamson's 102 provided a rare moment of cheer on a truncated day when play was restricted to 23.1 overs with only 54 runs scored.
That was the only wicket to fall as the hosts increased their lead to 171 after England were all out for 58 on day one.
Bleak weather in Auckland over the last two days - only 26 overs were possible in total on days two and three - could force New Zealand to declare on a total of less than 300 for only the sixth time in their history.
He was still on 100 when the rain swept in for the first time but when play resumed an hour later, after a revised tea break, he added only two more before being trapped in front by Anderson. Only 17 balls were bowled on Saturday before showers returned for the entire day.
"The important thing is what happens in the rest of the game and the confidence of the players, trying to clear your minds", Thorpe said.
By then, he had provided England's batsmen with an object lesson in the patience required to negate early lateral movement - of which the visiting attack found much less than New Zealand's Trent Boult and Tim Southee - before cashing in on a pitch of easy pace and true bounce.
The second test, a standard daytime match, is at Hagley Oval in Christchurch from March 30 to 3 April.
"We didn't play the swinging ball well, no-one did and we weren't able to put a foothold in the game", he said.