Leandro Paredes was judged to have been hauled down to the ground by VAR, with Lionel Messi tucking home the spot-kick in the 10th minute.
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It was eerily similar to England defender Harry Maguire being dragged to the floor in Monday's 6-2 win against Iran by Rouzbeh Cheshmi in their World Cup opener.
The Three Lions were not awarded a penalty, though they ended up giving away one when John Stones was deemed to have fouled Morteza Pouraliganji in the box with minimal contact.
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It led England legend Gary Lineker to state Iran were given the spot-kick out of sympathy having been hit for six by Gareth Southgate's men.
But the consistency of match officials has again come under scrutiny as Paredes was given a penalty when England were not, with the blatant foul not even going to review.
Speaking on commentary for talkSPORT 2, David Connolly said: "There's going to be an awful lot of penalties at this World Cup.
"That one was more similar to the Maguire one than the one John Stones gave away."
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Taking to social media, one baffled fan tweeted: "Argentina awarded a penalty for exactly the same incident on Harry Maguire yesterday that wasn't even reviewed. The inconsistency!!!"
Another posted: "That foul on Paredes was the same as that foul on Harry Maguire but England didn't get a pen."
A third added: "If that grab on Paredes is a pen then certainly Maguire's should've been yesterday."
One supporter simply stated: "The inconsistency. Maguire no penalty. Paredes penalty."
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After being awarded the penalty, Argentina made no mistake from the spot as Messi rolled it into the bottom left corner.
The Paris Saint-Germain forward, who has now scored in four World Cups to tie with Pele and Cristiano Ronaldo, then thought he had another.
But his 22nd minute strike was ruled out for offside, with Lautaro Martinez the next to have an effort chalked out by VAR for offside moments later.
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And Martinez yet again was judged to be offside in the 34th minute after he rounded the goalkeeper before tapping into an empty net.