The Kiwi opener Fulton sixth half-century and a rollicking 71-run stand for the eighth wicket between Brendon McCullum and James Franklin helped New Zealand reach a challenging 263-8.
Left-arm spinner Daniel Vettori bagged four wickets as New Zealand dismissed debutants Ireland for 134 to post their sixth successive win in the tournament, including three in the first round.
Defending champions Australia and New Zealand are the only unbeaten sides with eight points from four matches. They are followed by Sri Lanka (6/4), South Africa (4/4), England (2/4), the West Indies (2/4) and Bangladesh (2/4).
Ireland never looked like threatening New Zealand's total despite an entertaining 75-run stand for the fourth wicket between Kevin O'Brien (49) and brother Niall O'Brien (30). Kevin smashed three huge sixes in his 45-ball knock.
Fast bowler Shane Bond rocked Ireland with two quick wickets in his lively opening spell, removing William Porterfield and Jeremy Bray to eventually finish with 2-18 off five overs.
Vettori and off-spinner Jeetan Patel (2-32) kept non-stop pressure on Ireland, who lost their last seven wickets for 24 runs.
Earlier, Fulton's responsible knock and a late flurry of boundaries from wicket-keeper McCullum (47) and Franklin (34 not out) put paid to Ireland's hopes of restricting New Zealand to a modest total.
It was New Zealand's depth in batting that thwarted Ireland who reduced the opposition to 189-7 in the 43rd over before losing their way in the closing stages, with 45 coming in the last three overs.
McCullum's 37-ball knock contained a six in the last over that smashed a window-pane in one of the boxes, while Franklin hit one six and three fours in his 22-ball innings.
Seamer Dave Langford-Smith (2-41), and off-spinners Kyle McCallan (2-35) and Andrew White (2-45) had bowled with discipline to raise Ireland's hopes of containing New Zealand despite Fulton's half-century.
The New Zealand opener regained form with a well-paced innings just when his team-mates had been struggling for runs against Ireland's disciplined seam-spin comination.
Fulton, a middle-order batsman opening the innings in the World Cup, had made only 62 in his last three matches before playing a valuable innings.
New Zealand were not allowed to build a partnersip as skipper Stephen Fleming (10), Hamish Marshall (16), Scott Styris (10), Craig McMillan (22) and all-rounder Oram (20) all got starts, but none could play a long knock.
New-ball bowler Boyd Rankin provived the breakthrough in the sixth over when he dismissed Fleming, who was caught cutting at point by Porterfield.
Langford-Smith then struck twice in the space six overs to put New Zealand on the back foot, removing Marshall and Styris.
New Zealand found runs hard to come by when Irish skipper Trent Johnston introduced his spinners into the attack, as McCallan and White kept a tidy line and length on a slow track.
McCallan was rewarded for his discipline when he got rid of McMillan and well-set Fulton, who was adjudged leg-before.