Williamson’s 35-ball 61 propelled New Zealand to 185-6 and their bowlers kept Ireland down to 150-9 to top Group 1 with seven points after their final Super 12 match in Adelaide.
Australia, who next play Afghanistan at the same venue, and England can go level on points with New Zealand if they win, but the Black Caps have a far superior net run rate.
Only a mathematical miracle can push last year’s beaten finalists out of the last four now, leaving Australia and England to scrap it out.
“A really good team performance, which was required. We knew what Ireland were capable of, they have played some stunning cricket,” said Williamson.
The captain led from the front, having failed to convert starts in the earlier matches, as New Zealand dominated on a sunny afternoon despite a stunning hat-trick by Ireland fast bowler Joshua Little.
New Zealand were cruising at 174-3 in the 19th over when the left-arm quick removed Williamson, James Neesham and Mitchell Santner on successive balls.
It was the second hat-trick of this edition of the World Cup after Karthik Meiyappan of the United Arab Emirates against Sri Lanka in round one.
Little’s strikes checked New Zealand’s surge, but Williamson, with his first fifty of this tournament, had already put his team on course for a challenging total.
Daryl Mitchell hit an unbeaten 21-ball 31 and put on a key partnership of 60 with Williamson, who was under scrutiny for his slow batting but smashed five fours and three sixes in his 35-ball knock.
Finn Allen and Devon Conway started cautiously against a disciplined Irish bowling attack after being invited to bat first.
Allen broke the shackles in the fourth over as he smashed leg-spinner Gareth Delany for three fours including two on consecutive deliveries.
He kept up the charge and hit a six and four off fast bowler Mark Adair before the bowler got him caught at mid-off on the next ball as the Kiwis reached 52-1 at the end of six overs.
The left-handed Conway found it tough to accelerate despite a couple of boundaries but stood in a 44-run stand with Williamson.
New Zealand lost their way in the middle with Delany taking two wickets including Glenn Phillips for 17, but Williamson soon took charge.
Irish pride in defeat
Paul Stirling (37) and Andrew Balbirnie (30) got the Irish off to a flier in their opening partnership of 68 off 49 balls.
The giant-killing Irish team had taken down two-time champions the West Indies in round one and then shocked England in a rain-hit Super 12 clash.
But Balbirnie chopped one onto his stumps off Santner and fellow spinner Ish Sodhi bowled Stirling in the next over to douse Ireland’s hopes as their chase fell apart.
Fast bowler Lockie Ferguson returned figures of 3-22 after a double strike in his fourth over. Santner, Sodhi and fast bowler Tim Southee took two wickets each.
“We bowled pretty well, but our fielding has been a bit off in the tournament,” said Balbirnie.
“The guys have played really well. We have been happy with the effort.
“We caused a couple of upsets, we are playing better cricket than we were in the last 12 months, everyone is starting to show their class.