A series win over West Indies last December started their most recent run, before the Black Caps beat England in March, and most famously, triumphed over Pakistan last month in the United Arab Emirates.
Black Caps batting coach Craig McMillan says a fourth straight series victory would mean a lot to the side.
"I'm very proud of our home record, and I guess that's one of the challenges for us now – this is a one-off test match, where the series is on the line, so there's a lot for the side to play for. That would mean a lot to the team in terms of that consistency of winning over a period of time against some very good opposition."
The Black Caps will likely name an unchanged XI for the test, with the make-up of the bowlers likely the only selection debate. In the five tests played at Hagley Oval, spinners have only taken two wickets in 73 overs, with the Black Caps' predicted seam options – Trent Boult, Tim Southee, Neil Wagner and Colin de Grandhomme – taking 86 of the 92 wickets the Black Caps have claimed at the ground.
That history of seam success provides a chance for Matt Henry to be added into an all-seam attack, but it's likely the reliable spin of Ajaz Patel will be retained to provide greater variety.
McMillan predicts the wicket should provide plenty for the seamers, especially early in the test.
"You know what you're going to get at Hagley – it generally has pace and bounce, which is something we're always looking for – it suits the bowlers, suits the batsmen, and provides good cricket.
"History says generally you win the toss here and you bowl, but there's been plenty of times where we haven't won the toss and we've had to bat first. Quite often that first session is crucial, especially if the sun's out and there's a bit of wind about; it can actually be a very good batting track later in the day.
"It will be challenging for that first session - and that will be the key."