Their 5-1 win in the first leg at home meant it was always going to be near-impossible for the Kiwis to stage a comeback, and after a frenetic, end-to-end start, El Tri's quality began to shine through.
A first-half hat-trick from Oribe Peralta put the tie beyond the reach of Richard Herbert's men, and despite a late-goal flurry from the home side, New Zealand bows out second-best.
The home crowd turned up in their droves to cheer the All Whites on in style, and they found their voice early when Marco Rojas embarked on several dazzling dribbles through the centre of the pitch.
All that was lacking was the final twist, turn or pass, and New Zealand may have struck first, but Mexico's three central defenders held strong to ride out the early pressure.
It took the visitors 15 minutes to fashion a clear-cut chance, but they took the first one on offer: Carlos Pena slipped a delicate through-ball into the box for Peralta to finish, and his chipped effort took goalkeeper Glen Moss by surprise.
It was at that point the floodgates opened, as Raul Jimenez missed two one-v-ones either side of Peralta's next strike. El Tri galloped forward down the left and a low cross placed it on a platter for the in-form man. A near carbon-copy attack three minutes later led to a hat-trick-sealing strike.
Jimenez missed a third one-v-one as the half began to draw to a close, and Jeremy Brockie failed to take advantage of the visitors' profligacy as he fired a penalty straight into Moises Munoz's arms.
The second half started with a flash as chances were created at both ends, but after a similarly frantic opening period, Mexico managed to get hold of the ball and slow the tempo.
Sitting on a 3-0 (and 8-1) advantage, El Tri appeared eager to play out the remaining 40 minutes with consummate ease, but the snappy home side continued to make life difficult for their opponents in a committed, gritty display.
Coach Richard Herbert sent on more attacking options to force the issue and appease the home crowd, and Chris James finally delivered a goal when he expertly converted the Kiwis' second penalty of the day.
What followed was a crazy few minutes in which Rory Fallon and Carlos Pena both netted, making for an astonishing final scoreline of 4-2 (9-3 on aggregate).