Contact tracers were scrambling to track down any people in the community that may have been exposed.
"The rise is global cases means that people getting into a plane will reflect, in general terms, the level of transmission in the country they're coming from," Baker said.
"So that's really raised the stakes - and we've been seeing a steady rise in the number of people testing positive on arrival in New Zealand over the last few months."
More than 100 cases have been detected at the border already this month - roughly the same number as recorded across the months of November and December respectively - and 18 cases were reported in a single day on January 7.
"If you put this together with the fact the people will be increasingly infected with these more transmissible variants, it does markedly increase the risk of failure at the border, or in managed isolation and quarantine (MIQ)."
The number of travellers coming into New Zealand meanwhile remained at MIQ capacity - and that was expected through to at least this time next month.
"This virus is evolving very rapidly and takes advantage of every opportunity it gets - so it's critical that we get ahead of it," Baker said.
"I think we need a major upgrade and our response to the border, or we really do risk having a serious outbreak in New Zealand, before we get a vaccine."
Baker and his Otago colleagues have urged the Government to "turn down the tap" on travel from mass-infected countries.
That included implementing a five-day pre-flight hotel quarantine, with at least two tests, and reducing the number of available MIQ spaces.
Newly arrived people spending longer than two weeks in MIQ was also an option.
Professor Shaun Hendy, whose Te Punaha Matatini team is currently modelling risk for the Government, agreed New Zealand could expect to see further breaches.
"I definitely agree with Michael that, given current settings, we're going to continue to see cases like the one we've just had," Hendy said.
"And there's a chance that one of those will turn into an outbreak that's more like the Auckland August cluster.
"So, with what we're doing at the moment, we're certainly running the risk of another outbreak that requires a lockdown to deal with."
Hendy has previously pointed out that a community outbreak involving one of the new variants would likely require a full level 4 lockdown.
He added that tightening of the testing regime for new arrivals would have already helped reduce the risk - and there was the potential for follow-up tests after leaving MIQ to bring it down further.
Another positive was the fact there hadn't been another spate of infected border workers since a mini-cluster last year.
"That does suggest that, despite the ongoing testing regime, perhaps we are getting better at managing the risk for these workers."
Looking ahead, he said the Government would have to carefully consider a mooted travel bubble with Australia, a generally low-risk country where most people entering MIQ were coming from.
"One of the big potential downsides of that travel bubble is, if Australians don't have to go through MIQ, you quite likely might find [MIQ] filling up with a lot more cases."
Kiwis could play a part in reducing the risk themselves by actively using the NZ Covid Tracer app, with Bluetooth function on, and also being vigilant about hygiene.
