I found one where white after 12 moves were a pawn up, but had only moved pawns, king and a knight to c3 (but the knight had been exchanged). Doesn't quite fit the description (for several reasons), but I thought it sounded somewhat similar.
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Tough one this, perhaps.
I recall being impressed by a game in my youth which I thought was from a world championship match (might have been a knockout match leading to the championship), where the player of the black pieces (who I think was Tal) played only pawn and queen moves in the opening (10-12 moves perhaps) and won a pawn, but lost the game. [The game must have been 1960s or earlier]. I thought the other player was Botvinnik.
Quite a distinctive description but I have been unable to identify this game. It could be that I am wrong about some part of the description, but I am most sure of the facts about what pieces black moved and the fact that a pawn was won!
I'd be really pleased if someone can recall what game this was.