Louis van Gaal’s side looked to be down and out in the searing heat of Fortaleza after Giovani dos Santos had fired Mexico into a 48th-minute lead and goalkeeper Guillermo Ochoa continued his heroics as the last line of defence.
But the European nation dragged themselves level in the 88th minute as Sneijder lashed home a venomous strike from the edge of the box and then went ahead from the penalty spot in the fourth minute of added time after Arjen Robben was felled in the box by Mexico captain Rafael Marquez, with substitute Huntelaar calmly sending Ochoa the wrong way.
Van Gaal, who will take over as Manchester United boss once Holland's World Cup campaign comes to an end, demonstrated he is happy to make the big calls in the key games, as he withdrew skipper Robin van Persie 14 minutes from time at the Estadio Castelao for match-winner Huntelaar.
Holland were forced into a very early change in only the ninth minute as Nigel De Jong limped out of the action to be replaced by Bruno Martins Indi, before Robben’s incredibly hopeful appeals for a penalty were waved away when his attempted cross struck Marquez from point-blank range.
Mexico then ramped up the pressure and Hector Herrera was inches away from breaking the deadlock after being set up by Oribe Peralta on the edge of the box, with his slightly scuffed effort rolling just beyond a remarkably calm Jasper Cillessen’s post.
Herrera felt he should have been awarded a spot-kick after being caught in the head by the raised boot of Ron Vlaar with Stefan de Vrij’s studs also flying in as the Mexico man looked to head on in the area, but Portuguese referee Pedro Proenca awarded only a corner.
Cillessen was called into action again to palm away a long-range strike from Carlos Salcido, before a rare touch for the returning Van Persie saw him bring down a ball over the top before firing wildly off target.
After the first official 'cooling break' to allow both teams to take on some much-needed fluids, Dos Santos forced Cillessen into a decent save at his near post as the ball bobbled through to him somewhat fortuitously off the knee of Andres Guardado following an excellent flick from Peralta.
Marquez gifted possession to Van Persie in added time at the end of the first half but recovered to regain the ball with a very questionable challenge on Robben, which left Hector Moreno needing to be stretchered away after being caught in the tangle of legs in the box. Diego Reyes replaced Moreno for the second half.
The deadlock was broken in the 48th minute with a moment of sheer class from Dos Santos. The former Tottenham man chested down a loose ball well outside the Dutch area and then unleashed a half-volley as the ball sat up, his shot flying beyond the despairing dive of Cillessen.
The Dutch goalkeeper was called into action again to gather a curling effort from Peralta, before his opposite number Ochoa produced yet another breath-taking save to keep his side in front.
Ochoa, the hero of Mexico’s 0-0 draw with Brazil, somehow palmed De Vrij’s volley from inside the six-yard box away from the centre of the goal and onto the outside of the post after Robben’s corner from the left was met firmly by the defender.
Van Gaal’s side were now pushing hard for a leveller, with Sneijder seeing a shot from the edge of the box deflected narrowly wide, and the Galatasaray man was then just inches away from connecting with Robben’s cute cross from the left.
Peralta had the ball in the net for Mexico, but the whistle had already gone for offside, before Robben went to ground under a challenge from Miguel Layun, only for Proenca to again remain unmoved.
The Bayern Munich man stayed on his feet after hurdling a clumsy tackle from Marquez with 15 minutes to go but could not beat Ochoa as the goalkeeper blocked his effort from an angle with his feet.
Ochoa somehow blocked substitute Huntelaar’s close-range volley with time running out, although the offside flag had already been raised, but he could do nothing when Sneijder unleashed an unstoppable strike from the edge of the area after Mexico could not clear from a corner.
And in the fourth of six minutes of added time, Robben finally caused Proenca to point to the spot when he threw himself to the floor after his foot was caught by Marquez, allowing Huntelaar to step up and show nerves of steel to send Ochoa the wrong way from the penalty spot.
Holland will now return to Salvador - where they thrashed holders Spain 5-1 in their tournament opener - to face Costa Rica or Greece in the quarter-finals next Saturday.
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