Tehau, a delivery driver back home, became the first player to score for both teams in a Confederations Cup match having headed in for the Oceania champions after 54 minutes before finding his own net 15 minutes later in the Group B match.
Error-prone amateurs Tahiti, with only one professional player in their squad, suffered a terrible start when the ball hit the referee and ran to Nigeria's Uwa Echiejile who scored in the fifth minute with a twice deflected shot.
Nigeria seemed set for a big scoreline when Nnamdi Oduamadi strolled through Tahiti's defence to make it 2-0 five minutes later after the South Pacific islanders gave the ball away and he added a third for the African champions before the half-hour.
Tahiti brought the crowd to life, though, when Tehau headed a goal back before a previously wasteful Nigeria produced a late flurry when the unfortunate Tehau put through his own goal, Nnamdi completed a hat-trick and Echiejile scored his second.
"To lose 6-1 is hard but you have to put it in context," Tahiti coach Eddy Etaeta told reporters. "We are an amateur side playing against professionals and of course that showed.
"But when the draw was made in December I said if we scored one goal here it would be a great achievement and we have accomplished that."
Nigeria coach Stephen Keshi added: "They [Tahiti] said they were going to fight like lions and they did.
"But, with all respect to Tahiti, you think it's going to be easy playing against a team like that but they showed us they can play football and I congratulate them.
"We wasted a lot of chances in the first half but I am pleased we got the goals in the end."
The 20,000 crowd vociferously backed Tahiti, who took the field wearing shell necklaces, and jeered the Nigerians, creating a surprisingly raucous atmosphere at the Mineirao, especially considering FIFA's ban on musical instruments.
Nigeria could easily have been five goals ahead at halftime as they wasted further chances in a rather nonchalant fashion.
Tahiti strung some neat moves together and had the one-third full stadium in raptures when they scored in the 54th minute when Tehau headed in at the far post from a corner.
They were growing in confidence and Nigeria became visibly frustrated until the islanders ran out of steam in the last 20 minutes.
Nigeria arrived in Brazil on Sunday after a dispute with their national federation over bonuses sparked a players' boycott which briefly threatened their participation.
It was Tahiti's first match against opponents from outside the Oceania Confederation, according to official records, and one they will never forget, especially Tehau.
"Well I am so proud to score," he told reporters. "I saw the gap and went for it. We showed we could play some football, and yes we lost, but we deserved at least a goal and we got it.
"If I could chose one team to play for it would be Barcelona but I wont tell the Spain players that when we play th
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