The Italian headed home from a Steven Davis corner in just the 11th minute, before doubling his and Saints’ advantage on the half-hour mark with a composed finish.
But it was not just his two goals that led to praise from Koeman, with the Saints boss thrilled with his contribution all over the pitch.
“It’s a great corner from Davis for the first one and a great header, but the whole individual performance from Graziano was amazing.
“He was strong, he was winning battles and scoring and that is what you expect. It was a good reaction at the right time.”
After a tough couple of months in front of goal and with injury, Koeman was happy to see his striker show character to down the Potters.
“You need personality to come back. Graziano was struggling with some knee problems, but it’s always about confidence for strikers,” Koeman added.
“If he realises what he did here to score and fight for the team, then he will score more goals for us.”