When Burns departed for 45 runs, Brayden Hill (39 runs) and Oliver Kyle (34) kept Allen company before No 6 Baylee Foote (11 not out) closed their account on 365-5 in 45 overs.
Allen lost his wicket to the right-arm leg spin of Carl Miller, holing out to Matt Windle at deep cover on the last ball of the NBHS innings.
While he will be the first to confess Marewa's bowling wasn't the most frugal he has come across - they gifted 32 extras to the NBHS total - it does add the wow factor to know the teenager was playing in the colts division of the annual Napier Marist Old Boys' Invitational Sevens Tournament at Park Island, Napier.
"I played two games in the morning [for Marist Colts] so I had to leave that and go play cricket," he said, revealing that was always the plan, to leave about 11am although cricket is on a par with playing rugby during winter for the NBHS First XV team as halfback.
While batting, Allen realised he had carved up his 50 relatively smartly so he fancied his chances of going on to making his maiden century for the team but he never dreamt of flirting with a double ton, let alone making one.
"I knew I could turn it into a pretty big hundred."
When he crossed that bridge the batsman psychologically reset his mental clock.
"I just thought start from zero again and keep going."
Allen soon got to 150 runs and, with nine overs left, he thought it was time to go hell for leather in trying to post 200. Even if he didn't, he thought he would find comfort in a hefty score.
"It was a little bit disappointing and it would have been nice to not be out but ... yeah."
It was his ambition to score a century before finishing school at the end of the year.
However, Allen revealed that dream was close to evaporating as he approached the first century mark when he offered Marewa the only opportunity to end his innings.
"I was almost caught behind on 97 runs so I just got a bit lucky there," he said of Marewa wicketkeeper Brad MacDonald whose glove work just deserted him on the delivery.
Allen had quickly scrambled out of any mental quagmire to simply remind himself that he was given another lease of life so, with nothing to lose, make the most of his good fortune.
In fact, the hapless opposition skipper employed eight bowlers, including four overs from wicketkeeper MacDonald (1-33), to try to end the batsman's domination.
Foote was the best NBHS bowler, taking 3-16, including a maiden, to stymie Marewa's run chase to 146 in 23.3 overs.
Allen is on study leave and was surfing yesterday before sitting his second exam paper tomorrow but guessed his school would have acknowledged his feat at its weekly assembly.
He is having a gap year next year working as a log scaler and isn't sure what he wants to do if he attends university.
A former Hawke's Bay representative cricketer from under-12 to 15, he hopes to earn a place in another age-group team.
For the record, HB Cricket chief executive Craig Findlay said Ryder had scored 270-odd runs for NBHS First XI against Rotorua BHS in the Super 8 competition at the same wicket, before his school went on to claim the crown that summer.
Thompson had scored an unbeaten 205 for Lindisfarne College First XI to smash the record of the highest individual innings registered at Cornwall Park, Hastings, against the senior Cornwall CC team in January 2013.
