Sri Lanka were 45 for one at the close of play on Tuesday, needing another 345 runs on the final day after Williamson and BJ Watling had turned the game in the hosts' favour with a world record sixth-wicket partnership of 365.
"Obviously the wicket was a very good batting surface," said Williamson, who scored a career-best 242 not out. "We have got to come back tomorrow and bring our 'A' game to dismiss a strong Sri Lankan batting lineup.
"They showed in the first innings they were more than comfortable on that surface.
"If we can get a couple early tomorrow that will put us in a very strong position but I think patience is key because it is a good surface.
"But if you get one (wicket) then things can happen quite quickly so who knows how tomorrow unfolds."
Sri Lanka need to win the game to level the two-match series after New Zealand won the first test in Christchurch.
The highest successful run chase batting last on the Basin Reserve is the 277 for three that Pakistan achieved in 2003.
Opener Kaushal Silva will resume on 20 on Wednesday along with nightwatchman Dhammika Prasad, though he gave several hints late on Tuesday his stay at the crease may be short, which will bring Kumar Sangakkara, who scored 203 in the first innings, to the wicket.
"We are going to have to work hard to take nine more wickets," Williamson added, aware of the threat Sangakkara will pose.
"If we bowl in the right areas like we know we can (we can) create opportunities, but anyone with Kumar Sangakkara in their team can have confidence so I think it's set up for a good day of test cricket."
(Editing by Sudipto Ganguly)
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