Kadiya completed his hat-trick with goals in the 50th and 68th minutes to give the home side a 3-2 lead.
The clock ticked down as a Ngongotahā comeback started to look out of reach - until Simiona stepped up to equalise.
Ngongotahā coach Andrew Gibbs said his players showed the "Ngongy heart" on Saturday.
"It was outstanding. We had all sorts of disruption this week and had players pull out on the morning of the game. We lost one of our star midfielders Cuba [Casas] 30 minutes in, he went out with a suspected ACL injury.
"Jason Walker had a bit of a hamstring strain from last week, but thought he'd be alright. That went pretty early on, but we only had one player on the bench, so he ended up playing most of the game on one leg.
"To actually come back from being 3-2 down and equalise on the road against a big club like Albany, who are in the top four, I'll take a point every day of the week."
He said all the Ngongotahā players that were available were forced to work hard, but Scott McKnight in particular put in a big effort.
"Young Scott played his first full game for us, he's had hardly any training throughout the year because he's been busy with other stuff through school and things.
"He's only a young guy, but he played the whole game and it was a marathon effort, being thrust into a key position and working his butt off the whole game. He looked knackered by the end, but he just kept giving and giving."
Ngongotahā host Bucklands Beach next week before travelling to Franklin United in the final round.
"I'm very confident we'll be able to do a job against Bucklands at home next week and if we do that I think we'd be favourites to go and beat Franklin, for a second time this season," Gibbs said.
NRFL Division Two Results
Bucklands Beach AFC 0 Takapuna AFC 0.
Northland FC 0 Cambridge FC 2 (Josh Clarkin 80', Jamie Woodlock 85'). HT 0-0.
Franklin United 4 (James Hoyt 33' 63', Salesh Kumar 40', Charlie Heather 56') Te Atatu 0.
HT 2-0.
Onehunga Mangere United 0 Papakura City FC 2 (Rajnesh Sharma 6', Cory Mackay 15').
HT 0-2.
Albany United 3 (Herve Kadiya 23' 50' 68') Ngongotahā AFC 3 (Yamil Casas 8', Aaron Lawrence 45+3', Harlem Simiona 88'). HT 1-2.
Metro FC v Claudelands Rovers – Match abandoned due to unplayable pitch