Now that New Zealand have done the hard work, they can't afford to let their momentum slip when playing the minnows of Canada and Bangladesh in their remaining games at the World Cup.
The prospective loss of points from the Kenya game allows no margin for error and while New Zealand should be safe from missing the Super Six, the issue is still not beyond doubt.
Every possible advantage in terms of run rate must be utilised by the TelstraClear Black Caps, and at the same time that involves ensuring that some of the key players for the later matches get quality time in the middle.
New Zealand has had a great challenge in the first three games of their tournament, but they are not even halfway up the mountain yet.
Yesterday's outstanding win over South Africa highlighted the ability in the side.
This was one of the great fightbacks.
It may be that some look at the Duckworth/Lewis involvement and claim that it helped New Zealand.
To do so would be to ignore the basic fact.
New Zealand were so far in front of the D/L requirement that once the game was reduced to 39 overs they were never in danger of missing out on a win.
Often, the D/L method has been criticised because it favours the team batting first.
But those with memories long enough to recall what happened when teams batting second in the past were virtually handed matches without having to work for victory will appreciate that here was a classic example of using the method to advantage.
New Zealand put such outstanding pressure on the vaunted South African attack that the home team were baffled and didn't really have a response.
New Zealand teams in the past have not generally provided these sorts of problems for South Africa.
It was a classic example of everything coming right on the day, with the obvious key point being captain Stephen Fleming's outstanding innings. There were signs during the Indian series at home, that there was greater things around the corner from the captain, more from the types of shots he was playing, than from anything else.
That was borne out from some of the classical strokes he played so effortlessly, with the great advantage of timing, during his 134 not out.
There is something to be said also, for the quietly assured approach Nathan Astle has been taking in the matches against the West Indies and South Africa.
Two 40-plus scores with an increasing confidence in stroke making suggests he is much more comfortable on the World Cup stage than has previously been the case in his career.
The signs are better from a batting perspective.
The bowling was put to the sword by the South Africans, but clearly the pitch was a factor in that as evidenced by the home team suffering similarly. What is needed is for more bowling consistency in the remaining pool games.
It is also to be hoped that the back spasms suffered by Daniel Vettori are not something that New Zealand cricket overall should be worrying about after the problems he suffered three years ago.
Fleming's men have seized the initiative, the challenge ahead of them is to make sure they do not repeat the fault of many of their predecessors and let it go.