The Pacific Islanders went behind in unfortunate fashion. Echiejile hit a speculative effort from distance, which first struck Jonathan Tehau before hitting Tahiti captain Nicolas Villar to take the ball past a stranded Xavier Samin.
Nigeria then doubled their lead with a well-taken effort by Nnamdi Oduamad. A slack Tahiti pass was pounced upon and the ball found its way to the forward, who calmly slotted home.
Nigeria extended their lead shortly after. Ahmed Musa broke down the left and his rather tame cross was spilled by Samin, allowing Oduamadi to tap home the rebound.
There were loud cheers as Samin partially made up for his earlier mistake after a brave challenge at the feet of Anthony Ujah, who found himself one-on-one with the Tahiti goalkeeper.
The moment of the game came when Tahiti scored their historic goal. The side's only professional player Marama Vahirua whipped a corner to the back post, where a rising Jonathan Tehau thumped his header past Vincent Enyeama.
The celebrations by the players on the pitch and from coach Eddy Etaeta on the sideline were something to behold, as the Tahitians revelled in the limelight.
They were quickly brought down to earth though, as the goalscorer of that historic effort poked an Oduamadi cross past his own goalkeeper, with Brown Ideye applying pressure.
Oduamadi then wrapped the game up, and claimed the match ball, completing his hat-trick with a simple tap-in, with Echiejile completing the rout with his second.
Nigeria will face a sterner test when they come up against South American champions Uruguay in their next game. Tahiti, meanwhile, face the small matter of a trip to the Maracana to face FIFA World Cup™ holders Spain.