Worryingly for New Zealand, no batsman has scored a century in the first two tests, with Williamson's 77 the highest individual score by the home side during the series. Brendon McCullum is averaging 57.33 with two 50s and Taylor has been consistent without cracking a big hundred.
New Zealand have struggled with the four-prong pace attack of the Proteas made up of Morne Morkel, Dale Steyn, Vernon Philander and the seemingly ageless Jacques Kallis.
Taylor said, although the result may have been lopsided in Hamilton, he didn't think his side was far off the pace and they just needed to execute their plans better.
"I think we've still got to stick to the basics and play. Whatever we do first, we've got to do it well in the first session. Obviously we are 1-0 down in the series. We know we are not far away from competing with this side. We've been on top in a few situations, we just haven't been able to ram it home. Whatever we do first, we've just got to do it well.''
The game has similar overtones to the historic victory against Australia in Hobart in December.
Taylor said the side had spoken about Hobart briefly during the week, although the shape of the team for tomorrow's test will be different with a change away from the four seamers approach in favour of strengthening the batting order.
Mark Gillespie, Chris Martin and Doug Bracewell appear the likely pacemen, with Daniel Vettori to provide the spin bowling, while Dean Brownlie and Williamson will fill in a few overs when required. Recalled batsman Daniel Flynn is expected to open the innings with Martin Guptill.
South African captain Graeme Smith said his side were eager to finish their time in New Zealand on a high note.
"We've obviously played extremely well on this tour in all forms,'' he said. "We'd like to round that off with a comprehensive performance in the next five days. But those first couple of days are going to be a crucial aspect of that. The last test of a touring summer is always an important one. So we want to finish strong and hopefully get on the plane with a big smile on our face.''
Smith said there were no injury concerns within the camp and they would likely pick the same XI from the Hamilton test.
Follow Daniel Richardson on Twitter