Two-time champion Anderson, who was the favourite to win the third-round clash, claimed the first set at Alexandra Palace but faded as proceedings went on.
Nicknamed ‘Hollywood’, Dobey reeled off four sets in succession to earn a 4-1 win and set up an intriguing clash against Rob Cross or Mervyn King in the last 16.
While world number 22 Dobey was pleased with his display against Anderson, he also revealed a backstage conversation with the Scotsman irritated him and fuelled his stellar victory.
"Gary said something to us in the last break and I didn't like it. It annoyed me and there was no way he was winning the game after that," he told Sky Sports.
"I came out and tried to forget about it. He is a class lad, everyone knows that, but I didn't agree with what he said. I had one job and I made sure I was winning this game.
"It was a big win, Gary is a class lad, one of the big names in darts and has been for a while so it is a massive win.
"I never gave up. That's the kind of lad I am, always fighting to the end. I am delighted to get the win."
Dobey added: "After what was said on stage, you start thinking things but I came out to do one thing and got it done. I don't know if he was playing mind tricks but I am the winner. Who cares?!
"If he was playing mind tricks, he doesn't need to as he is a class act.
"Gary is straightforward, says what he thinks. If he has a problem he will tell you. He didn't have a problem with me but he couldn't say to whoever it was and it kind of got to us.
"I just tried to block it out."
Anderson’s exit sees him become another big name to crash out of the competition after defending champion Peter Wright was beaten by Kim Huybrechts on Tuesday.
Wright was also beaten by a 4-1 scoreline and after having no answer against the Belgian, who managed to open up the bottom half of the draw.
Elsewhere in Wednesday's afternoon session, Jose de Sousa (48) came from three sets down to beat Ryan Searle (35) 4-3 in a barn-burning match. In the other game Alan Soutar (44) racked up four straight sets of his own to down ninth seed Danny Noppert (31).
