A high-powered business delegation led by Mr Luxon was heading to Tokyo on Sunday via Papua New Guinea as the new government looks to grow trade.
However, the plane was deemed unable to get to Japan after the discovery of blown fuses on the NZDF Boeing 757, stranding the group, including Trade Minister Todd McClay, dozens of business leaders and journalists.
Mr Luxon was not caught up in the drama, legging it from Port Moresby along with three staff by taking last-minute commercial flights via Hong Kong to maintain their schedule in Tokyo on Monday.
Around 50 others were forced into an unscheduled overnight stay in the PNG capital as backup plans were made.
The solution: the NZDF plane would fly to Brisbane, where an re-routed Air New Zealand flight would pick up the delegation.
Defence Minister Judith Collins explained the plane was unable to make it to Japan, but a three-hour flight to Queensland was possible.
"This plane, without its spoilers, which had to be taken off, will only be able to fly at a lower altitude for what's necessary for those long haul flights," she told Radio NZ.
Air New Zealand's chief executive Greg Foran - one of those stuck in Port Moresby - ordered NZ99, a direct service from Auckland to Tokyo Narita, to make the stopover to pick up the stranded delegation.
The group will finally make it to Tokyo on Monday night, meaning Mr Luxon will have the opening day of the trip - which includes events with NZ Rugby, kiwifruit marketers Zespri and the space industry - alone.
The bungle was labelled as "keystone cops stuff" by New Zealand's most popular broadcaster Mike Hosking, with Ms Collins agreeing it was "embarrassing".
It could also prove to be expensive, with the government picking up the bill for the repairs, the stopover and most likely, getting the group home.
Mr Foran said the bill was a matter for another day.
"Let's get everyone there. We'll worry about what we're going to do financially when we get everyone there," he told journalists.
Ms Collins said the return travel was yet to be organised.
"We shouldn't count on (the NZDF plane) getting to Japan to bring back the prime minister and the delegation unless a miracle happens and suddenly it's fixed," she said.
The breakdown is the second in three months, with Mr Luxon making a similar last-minute switch to commercial flights in March to attend an ASEAN summit in Melbourne.Â
In recent years, the NZDF 757s have failed Jacinda Ardern on visits to Washington DC and Melbourne, and cancelled a day of John Key's 80-strong delegation to India, with a similar issue discovered on a stopover in Townsville.
There is a raging debate in New Zealand as to whether it can afford to replace the planes, which are primarily used for defence business, and are seconded for use by the prime minister on trade missions.
They are due to be replaced in 2028, though a defence capability review - due this month - may recommend bringing that timeframe forward.
Ms Collins said the defence force was "doing an amazing job with planes that might otherwise be retired", appealing to opponent parties to back their replacement.
"No prime minister wants to spend an awful lot of money on something that's seen as 'nice to have' by some people," she said.
"But we have to build the economy (and) it is really important the PM and business people can get out."
