Daniel Sturridge ultimately claimed a point for the visitors with a 72nd-minute header from Suarez's cross, but even that could not spoil Dummett's day.
He said: "It's something that every boy would dream of doing, scoring at St James' Park at the Gallowgate End.
"I was looking at the crowd when I was running away. I didn't know what to do, I didn't know where to look. It was just unbelievable.
"I couldn't have asked for anything better. Making my debut was obviously something massive, and then scoring the goal to help the team get a 2-2 draw...
"But at the end of the day, it's a team game and we worked well as a team to get a good point."
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