The hosts had managed to get their first goal of the game thanks to a deflected shot from Diaz in the first half.
Despite their dominance of the ball, Guardiola's men were stuggling to find the right finish as the second half went on.
They managed to find a way after Sane played Gabriel Jesus through on goal, with the Brazilian international weaving through before getting a shot away.
That effort was well tipped on to the post by Sergio Rico, but it fell to Diaz in the box who smashed the ball past the Fulham defenders on the line.