The Frenchman overtook Luis Aragones' record of 173 by scoring his 174th against Real Madrid in the Spanish Super Cup.
Griezmann made the score 2-2 at the end of a frantic first-half against their fiercest rivals.
Atleti had taken an early sixth minute lead through Mario Hermoso, but Real replied through Antonio Rudiger and Ferland Mendy.
Griezmann then had his say, switching passes with Koke before running into plenty of traffic.
However, despite having Rudiger and Luka Modric all over him, the World Cup winner fooled them both, and left the latter on the floor with a brilliant turn.
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Then unleashing a right-footed shot, Kepa Arrizabalaga could do nothing about the record goal, seeing it fly past him into the corner of the net.
Griezmann overtakes Aragones, best known by younger fans as Spain's Euro 2008-winning manager.
Fernando Torres is also on the list, but down in sixth on 129 goals.
Like Torres, Griezmann reached his total over two different stints, having an unsuccessful two-year stint away at Barcelona.
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Returning to Madrid in 2021, he's since gone from traitor to club icon, and his feeling towards the fan base is mutual.
When asked about a contract extension, the 32-year-old said: "Yes, that's what I said. I know the club is in favour of being able to make an effort and we will talk about it.
"Beyond Europe, what I would like later is MLS, I've always recognised that.
"But Atletico will be almost 100 per cent my last club in Europe. It's where I want to be, where I look the happiest and here I am at home."