A large and lively Guyanese crowd witnessed Nathan McCullum win the game by hitting paceman Lasith Malinga for six over long off.
New Zealand needed 20 off the last two overs, chasing Sri Lanka's 135 for six on a slow track which included an outstanding 81 from opener Mahela Jayawardene.
Jesse Ryder's 42 off 27 balls got New Zealand off to a decent start but some intelligent bowling and smart fielding from last year's runners-up Sri Lanka kept things tight until, with three runs needed from the last two balls, McCullum struck.
Ireland, meanwhile, crumbled to 68 all out, falling to a 70-run defeat to West Indies.
Darren Sammy was the match-winning all-rounder for the hosts, making a top score of 30 with the bat, taking three wickets and four catches to delight a packed home crowd.
As organizers had promised, relatively cheap ticket prices and less stringent regulations resulted in a large and enthusiastic crowd but for a period it looked like they might merely witness another sorry episode in the decline of Caribbean cricket.
West Indies were without skipper Chris Gayle who pulled out with a neck injury and after none of their top order batsmen managed to get into their swing they were struggling at 93 for six.
The damage had been done mainly by 17-year-old slow left-armer George Dockrell, who bowled beautifully for his 3-16 from four overs, which included the wicket of Ramnaresh Sarwan (24) just as the Guyanese batsman had looked ready to step up the pace.
The crowd were given something to cheer about though by Sammy, surely one of the most under-rated all-rounders, who came in to make 30 from 17 balls helping the team, led by stand-in skipper Dwayne Bravo, to a reasonable total of 138 on a slow track.
Ireland simply never got going with the pace of Ravi Rampaul (3 for 17) and Kemar Roach reducing them to 16 for four and when Sammy (3 for 8) and Bravo (2 for 5) dealt with the middle order it was all over.
"We were right in it at half time, but it was just disappointing with the bat," said Ireland skipper William Porterfield who had begun the slump when he went to a brilliant Sammy catch off Roach with the second ball of the innings.
"We were right on the back foot after losing those three early wickets," he added.
Bravo said he hadn't been worried after the mini-collapse had given Ireland hope of dismissing West Indies cheaply.
"I had faith in the lower order, I knew once we got over 130 it would be difficult to chase," he said.
Bravo added that the hard-hitting Gayle would be back for the game against England, the third team in group D on Monday.
