The Black Caps' 35-run win in Adelaide likely means they will top their Super 12s group as, while England and Australia may yet equal their seven points, the Kiwis have a far superior net run-rate.
Only freakish margins of victory in both Australia-Afghanistan later on Friday and England-Sri Lanka on Saturday could deprive New Zealand of a spot in the last four, but they were given a test by Ireland.
Kane Williamson found some fluency at the crease and top-scored with 61 off 35 balls but New Zealand were pegged back towards the end of their innings by some fine death bowling, most notably from Little.
The left-arm seamer snared Williamson when the New Zealand captain miscued a pull to deep backward-square leg before pinning both Jimmy Neesham and Mitchell Santner in front off the next two balls.
The trio of wickets in the penultimate over halted New Zealand's charge to a 200-plus score as they settled for 185 for six and there may have been minor alarm as Ireland started the chase well.
Paul Stirling and Andy Balbirnie put on 68 in eight overs before the latter dragged on to his stumps off slow left-armer Santner before fellow spinner Ish Sodhi's googly did for the other Irish opener.
Santner and Sodhi kept a check on Ireland's scoring and took another wicket apiece while Lockie Ferguson finished with three for 22 as New Zealand cruised from that point on.
Tim Southee also chipped in with a couple of wickets as Ireland finished on 150 for nine.
Ireland have had a memorable past few weeks, with wins over the West Indies and England, but they will finish outside the top four of the group, meaning they may have to qualify for the 2024 tournament.