Graham arrived from Swansea City in January 2013 in a £5million deal but has failed to find the net in 24 Premier League appearances for the Black Cats.
He was instrumental in winning both penalties in the 2-1 win over Southampton on Saturday and Advocaat hopes this proves to be the turning point in the striker's fortunes.
"In training he's the best goalscorer, but in the games, he's not. That has to change," Advocaat said.
"He did a great job for the team (against Southampton). It was an unbelievable game in the way he worked and how dangerous he was.
"He did not score, but he did a great job for the team."