Argentina dug deep as the Cubans naturally began to tire, to tie the game and then score a double to get home 3-1.
Earlier Australia, who won the international tournament in Palmerston North last week, showed that was no fluke with a 7-0 blitz of Denmark with veteran Nick Shailes scoring four runs.
In other games Canada, who scored three runs in their first at-bat, held on against a plucky Venezuela 3-2; Japan were impressive in beating South Africa 11-0; while five-time winners USA had to hold on for a 1-0 win over Philippines.
All kiwi-fan focus was on the hosts in their important clash against the Czech Republic, delighted with Enoka’s blast over the fence to push New Zealand to a 3-1 advantage.
“The home run came with my third time up and I was just trying to hit the strikes and leave the balls,” said Enoka.
“I got lucky with that one and fortunate to get it over the fence. We were leading by a run so it was a game-changing aspect in the later innings and a bit of a spark for us not to die-off.
“It was a benchmark effort, a line in the sand. I think we can improve on today’s performance. It is going to get harder as we go on but the boys are tight and we will continue to stay connected.”
Czech Republic had two players on base in the bottom of the sixth but New Zealand pitcher Daniel Chapman managed to strike out Vojtech Forman to end the inning.
Hutt Valley’s Rhys Evans’ triple to deep left-centre bounced back off the fence but with the crowd cheering him on, Evans tried to run home but was tagged out to keep the score at 3-1 in the top of the seventh.
Josh Pettett then came on in the bottom of the inning and made it three-up and three-down to give New Zealand an opening win.
“It was really important to get that first win and get the monkey off our back,” said head coach, Mark Sorenson. “We played them last week and they came from behind to beat us and they will be a force over the coming years.
“I was really pleased with our pitching. We did not give up many hits but we gave up a few too many walks. And I was pleased we created opportunities but we did not create enough. I was pleased we scored the runs we did and that run by Ben was quite critical because it gave us the breathing room.”
Today New Zealand takes on USA in a key game at 3pm, with action beginning at 11am at Rosedale Park.
Scores, Day 1, Group A: New Zealand 3 Czech Republic 1, Argentina 3 Cuba 1, USA 1 Philippines 0
Group B: Canada 3 Venezuela 2, Australia 7 Denmark 0, Japan 11 South Africa 0.