All proceeded reasonably sensibly until the final 10 minutes when Time got busy.
Nine minutes from the end, another melee resulted in Nadi's goalkeeper Vereti Dickson and Kiwi player Lionel Taylor both seeing red.
Kiwi substitute Lawrie Letutusa was marched just before the end of normal time. To cap it off, Nadi's Napolioni Qasevakatini was ordered off.
Khem completed his hat trick in the sixth minute of stoppage time to level the scores then got his fourth in the 98th minute to secure the win, the first time Nadi had been ahead in the match.
A double from Mike Saofaiga - his goals arriving in the second and 21st minutes - and a further effort from Paulo Scanlan in the 10th had given Kiwi a 3-1 lead to put them on track for a memorable victory as the clock ticked towards halftime.
But Khem, and Time, had the last say.