The men - aged 36, 32 and 25 - were travelling south from Tennant Creek to Alice Springs on Saturday when they allegedly ignored the health order to stop at the checkpoint.
Police tracked down the 36-year-old and the 32-year-old on Sunday in Alice Springs.
They were each fined $5056 for breaching a health direction and ordered to get a COVID-19 test and isolate until they returned a negative result.
Officers located the 25-year-old on Monday and he was also fined and directed to isolate until he returned a negative test result.
"The actions of these three men has put undue pressure on our frontline staff and potentially risked the safety of the Alice Springs community," commander Lauren Hill said on Tuesday.
All three men have since returned negative test results.
The COVID-19 outbreak in the NT currently sits at 112 cases, with more expected.
It started when an infected woman illegally entered the territory in late October.
The 21-year-old was fined for lying on her border entry form as the virus spread from Darwin to Katherine, then to multiple Aboriginal communities.
It has now reached Tennant Creek, 1000km to the south of Darwin, where a lockdown has been extended for two days until Wednesday at 5pm.
Ali Curung Indigenous community, 170km south of Tennant Creek, also remains locked down.
Meanwhile, travellers continue to arrive in the NT after the territory opened its borders to fully vaccinated people and ended quarantine requirements.
Travellers wishing to enter the territory now have to return a negative PCR test taken a maximum of three days before their arrival.
They also need to get re-tested within three days of arriving and again on their sixth day in the NT.
Up to 3500 arrivals per day are expected by January.
Unvaccinated travellers have been barred, with only returning residents exempt.
Most arrivals must stay in high vaccination areas, such as Darwin and Alice Springs, for 14 days.
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