If several teams finished on the same number of points in the round-robin Super Eights second stage, then the net run rate would decide the pecking order for the semi-finals.
New Zealand, who had won all six of their previous World Cup matches in the Caribbean, have eight points in the Super Eights table including two carried over the first round.
They are level on points with Australia and Sri Lanka but lag behind both on run rate. South Africa have six points and England four, each with two games to play.
"You could lose by 30 or 40 runs in a tight game and that's going to affect your run rate massively down the track," Fleming told a news conference after Sri Lanka had beaten his team by six wickets.
New Zealand totalled a mediocre 219 for seven and Fleming knew his side's chances of winning would depend on penetrative bowling at the start of Sri Lanka's reply.
AGGRESSIVE STAND
But Sanath Jayasuriya (64) and Kumar Sangakkara (69 not out) shut the door on New Zealand by sharing an aggressive stand of 100 for the second wicket.
"The first 20 overs we just stumbled and bumbled our way through when we needed a great start," Fleming said. "From then on, it was a fine balance between trying to put pressure on them and look after our run rate."
Fleming delayed taking the third Powerplay -- when fielding restrictions apply so that the majority of the fielding team are grouped in an inner cordon around the wicket -- until what turned out to be the last over of the match, the 46th.
"The Powerplays were the toughest part," Fleming said. "If there are two hitters in and you use your Powerplay, you run the risk of your run rate being affected quite a lot.
"In a small game where there are only 70 runs to play with, it was important that we tried to grab a couple of wickets and still try to keep the Powerplays to a minimum.
"I wasn't willing to take the 10 overs of Powerplay and lose the game in the 38th over when you could stretch it out for another eight overs."
New Zealand, who need one win from their last two Super Eights matches to clinch a place in the semi-finals, play South Africa in St George's on Saturday and Australia on Friday, April 20.
Their defeat means only Australia, the holders, remain unbeaten in the seven-week tournament which culminates in the April 28 final in Barbados.
