After maintaining their unbeaten run at the tournament, they climbed to the top of the Super Eights standings thanks to a superior net run rate than champions Australia.
"We know we are capable of winning it, it's just about how we play on the day or how we let the opposition play," Fleming told reporters.
"As we get down to the business end -- we're in the semis or close to it by winning one more game -- it's going to come down to two games of cricket to win the World Cup.
"That's an exciting prospect but also a scary one as well. To get to that point we've got three tough games where players in form have to remain in form and we've got to be smart with our assessment of conditions."
New Zealand racked up 263 for eight on Monday and then grabbed the last seven Irish wickets for just 24 runs to bowl out the debutants for 134.
The result moved the Kiwis to within one victory of equalling their record 10-match ODI winning streak achieved in 2005.
Although New Zealand struggled at certain stages -- at 83 for three and 189 for seven -- Fleming praised Peter Fulton, who hit 83, and wicketkeeper Brendon McCullum for adding 59 runs to their total in the last five overs by scoring 47 from 37 balls.
"The fact we got to 260 (sic) was testament to our hitting power and Brendon McCullum's ability to hit the ball over the rope and into the gaps at the death."
New Zealand's next match is against Sri Lanka in Grenada on Thursday.
The seven-week tournament culminates with the final in Barbados on April 28.
