Otago struggled to put phases together in the first spell and were outmuscled at the breakdown by a determined Napier pack.
With Napier up by six points from the Spooner penalties, they were rewarded for their aggression when they blew over an Otago ruck inside Napier's half.
Halfback Uta Tupuola moved the ball down the right flank into the hands of Ollie Penno, who was brought down just outside Otago's 22. Tupuola fired a 30m bullet pass out to his outside backs, who put it through their hands finding some space for Paewai to score in the right-hand corner. Spooner missed the conversion and a penalty just before the break when Napier led 11-0.
Napier should have been up by another three points just before the break but turned down a kickable penalty 30m in front.
Otago captain Josh Renton said he was confident his side could turn the deficit around after the break.
"They beat us up in the first half and that was something we needed to work on and I think we did, in the second half.
"We were always confident and that wind was worth a lot of points and obviously we showed that and we just needed to hold onto the ball."
Otago were the first to score after the break through the boot of first-five Sam Ellis, who kicked with 100 per cent accuracy for a tally of 15 points. But it was Napier who scored the first try of the second spell, when left wing Shae Tucker carried two would-be tacklers over the line to extend the lead to 16-3.
However, the momentum began to turn thanks to the hard work of lock Troy Callander and blindside flanker Josh Dickson - the rangy forwards combined well to set up and score Otago's first of three tries.
Otago had an attacking ruck on the left-hand side of the field, 5m out from Napier's line. Renton fired the ball right to Callander, who was waiting out in the back line. He stepped inside his man and offloaded to a charging Dickson, who scored under the post.
The pair would use the same tactic a number of times throughout the spell to great effect.
Otago's next two tries were classic backline moves set up by Ellis, who put his outside men in space through sharp passing. Both Ben Miller and Aleki Morris were given room outside their men and showed pace and power to get to the line to score.
Although Napier captain Morgan Poi was disappointed with the loss he was proud of the effort the team put in.
"We started well, I think, with the wind in the first half. We got a few points but in the second half it turned to custard ... We definitely knew 11 points wouldn't be enough.
"Watching previous games of Otago, we've sort of noticed they start slow. So it was important to get points first but we really didn't get enough in the first half. But I'm definitely proud of the boys and their effort."
Otago will play St Kentigern College in Auckland on Saturday after they beat Hamilton Boys' High School 29-13.
Otago Boys' High School 30 (Josh Dickson, Ben Miller, Aleki Morris, tries; Sam Ellis 3 cons, 3 pen) Napier Boys' High School 16 (Kalin Paewai, Shane Tucker, tries; Trinity Spooner 2 pens) Halftime 0-11.