Du Plessis made a name for himself earlier this week when he batted for seven-and-a-half hours to help South Africa achieve an epic draw in the second test against Australia in Adelaide.
Sri Lanka, who started the day at 47 for four, still have some way to go to replicate that but moved through to 107-5 at lunch on the final day.
The Black Caps made one significant breakthrough in their search for a rare test win after five consecutive defeats, when Thilan Samaraweera was needlessly run out for seven.
Samaraweera, who boasts an average of close to 51, prodded a Doug Bracewell delivery wide of Jeetan Patel at cover and set off for what would have been a comfortable single, only for Angelo Mathews to stand his ground and leave Samaraweera well short of his crease.
It was a crucial wicket, meaning New Zealand were closer to getting into Sri Lanka's tail. But they were frustrated throughout the remainder of the session as Mathews (27 not out) and Prasanna Jayawardene (23 not out) tackled their work with a mixture of belligerence and occasional aggression on the docile pitch.
It was largely slow-going, with Sri Lanka batting at a run-rate of just 1.8 for the session, but run rate is far from their minds as they battle for survival.
