The winger went into a strop when subbed, while his club team-mate scored twice in the first half to better a late effort from Van Persie and give Low's side top spot in Group BNetherlands' hopes of advancing to the Euro 2012 quarter-finals are hanging by a thread after a 2-1 loss to Germany at Metalist Stadium on Wednesday.
A labouring Dutch outfit fell two goals behind by half-time thanks to a pair of lethal finishes from Mario Gomez, who took his tournament tally up to three, with both goals set up by Bayern Munich team-mate Bastian Schweinsteiger.
Bert van Marwijk's men were able to improve after the break though, and pulled one back through a breathtaking strike from Robin van Persie on 73 minutes.
But despite a late surge from the Oranje, Arjen Robben stormed off the pitch when substituted, allowing Joachim Low's men to hang on and take their place at the top of Group B.
Even if Netherlands beat Portugal in their final group game on Sunday, their fate is out of their hands, as
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The only change for both sides from their respective tournament openers came from Van Marwijk, who replaced Ron Vlaar at the back with Joris Mathijsen.
Van Persie retained his spot in the Dutch XI ahead of Klaas-Jan Huntelaar, despite the Arsenal striker's profligate showing in the 1-0 loss to Denmark on Saturday.
The 28-year-old had the first opportunity of the match after six minutes, running onto Mark van Bommel’s glorious lifted pass, only to poke his finish straight at Manuel Neuer.
Germany looked to respond through Mesut Ozil, whose volley from Van Bommel’s weak clearing header rebounded off the post into the grateful arms of Maarten Stekelenburg.
There was a real ebb and flow to the match developing, and Van Persie spooned another attempt off target after latching onto a pinpoint pass from Arjen Robben.
Van Persie's woes in front of goal seemed set to continue, and were further highlighted on 24 minutes when his German counterpart Gomez gave a lesson in clinical finishing.
Schweinsteiger’s through pass perfectly picked out the run of his club team-mate, whose exquisite turn allowed him the space to slot into the corner despite a slight touch by Stekelenburg.
Gomez came close to another just past the half-hour mark, but was a few inches short of connecting with Thomas Muller’s low centre from the right.
Germany were in the ascendancy, and could have doubled their lead when Ozil’s free-kick found Holger Badstuber completely unmarked, only for Stekelenburg to block the defender’s shot from point blank range.
The Mannschaft would get their second seven minutes before half-time though, with the Bayern combination working a treat once more.
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Gomez still had his work cut out for him after receiving Schweinsteiger’s pass on the right side of the box, but did not let the angle faze him, and lashed over Stekelenburg into the far side of the goal.
The Dutch goalkeeper was suspect for Germany’s second, but prevented his side from falling further behind by tipping away Schweinsteiger’s free-kick with the last kick of the half.
Van Marwijk shook things up at the interval, hauling off captain Van Bommel and Ibrahim Afellay for Huntelaar and Rafael van der Vaart to start the second-half.
However, Germany still held the upper hand. Mats Hummels surprised Netherlands with an enterprising run up the length of the pitch, before forcing Stekelenburg into a smart double save.
Robben tried to spark his side into life with a run down the left flank, teeing up Van Persie at the edge of the box for a shot that was pushed away by Neuer. Wesley Sneijder was next up, bending a long-range effort inches wide of the far post.
But as the second half wore on, Netherlands began to inch their way back towards contention. Robben sliced a volley off target, before Sneijder saw his shot blocked full on the face by Jerome Boateng.
With 73 minutes gone, they found a way back into the game. Van Persie took a pass on the edge of the box on the turn, and smashed an unstoppable shot with his weaker right foot past the despairing Neuer.
Robben was substituted to be replaced by Dirk Kuyt, and he appeared livid with the decision, throwing a look of disgust towards the bench before exiting at the opposite side of the pitch.
The Dutch then enjoyed a late spell of pressure, but Germany were able to hold firm at the back, and almost scored again after a gaffe by Stekelenburg nearly left Miroslav Klose with an empty net.