In wet and windy conditions, the French territory scored two unanswered tries and kept the Cookies scoreless in the second half.
The test was marred by ill-discipline, with Tahiti prop Martin Taeae, winger James Tekurio and Cook Islands centre Samuela Longo Leuta sent off amid a flurry of eight cards.
President of Tahiti Rugby Union, Charles Tauziet, claimed the "underdog" tag prior to kick-off but said the visitors ultimately won the game up front.
"We were strongest in the forwards and it makes a difference and after we have a game-plan that was better because we put two tries and Cooks put only three penalties," he said.
"I think we had a problem was ill-discipline - both teams - because during the game (there was) eight (players sent to the) bin - it was exceptional."
The President of the Cook Islands Rugby Union, Moana Moeka'a admitted it was a disappointing result.
"I guess we've got to move on from here and without having any Rugby World Cup pathway in front of us it's back to the drawing board and how we can actually make some progress on today's game," he said.
"The problem is we only play once or twice every two or three years...if you want to be playing international rugby you've got to be playing all the time. One, two, three games every four years is, in my view, just not good enough."
Tahiti will now face an Asian qualifier next year in a home and away playoff for a spot in the final World Cup repechage event.
Charles Tauziet was confident Tahiti's first ever victory against the Cook Islands will help them attract more sponsors and arrange more test matches over the next 12 months.
"Because the sponsors will be very happy with what we do - we come to Cook and beat Cook in Cook Islands - so I think they trust us now and we will have more sponsors and it will be more easy for us to organise a team, I'm sure, surely boost our budget towards the next round," he said.
"We have to work hard because we know the next step is higher and we have to watch our discipline and keep focused for the game."
Photo: Oceania Rugby Tahiti celebrate winning the 2017 Oceania Cup.