In his third appearance in a black and white shirt, the 31-year-old chose former club Boro as his first victims.
But the Australia international, who had insisted he would not over-celebrate if he found the back of the net, was relieved simply to have got off the mark.
He said: "I was so happy and excited when it went in, I really didn't know what to do. I suppose you could say I toned my celebrations down.
"But yes, it was special to me coming to the Riverside and scoring my first goal for Newcastle United - and it goes without saying that I'm hoping it was the first of many.
"I'm very pleased about it. It was nice to get off the mark. It was very important for me."