Pre-match favourite Anderson, who lifted the trophy in 2015 and 2016, was on course for his 50th tournament victory at the venue after taking the opening set.
But the Scotsman surrendered the early advantage and crashed out following an emphatic 4-1 defeat, having irked his former protege mid-match.
“Gary said something to us in the last break and I didn’t like it, so there was no way he was winning that game after that,” 32-year-old Dobey told Sky Sports.
“It kind of annoyed us. But I came out, the man I am, I tried to forget about it. He’s a class lad but I didn’t agree with what he said.
“I’m not going to say (what he said), it was just something I didn’t like. He’s one of the big names in darts and he has been for a while, so it’s a massive win.”
Unseeded Alan Soutar vowed to keep upsetting the world’s best after winning 12 of the final 13 legs to stun UK Open Champion Danny Noppert.
The Dundee firefighter feared he would “get battered” having fallen two sets down to Dutchman Noppert but battled back to claim a 4-2 victory and one of the best wins of his career, which included a superb 130 finish.
“He disappeared in the middle of the match and I took every chance I got,” Soutar, who will take on Germany’s Gabriel Clemens in the last 16, told PDC Darts.
“He’s world number nine, provisionally number eight, and probably a Premier League player, so for me to beat guys like that I love it, I absolutely love going toe-to-toe and taking people on.
“I’m unseeded and I will keep knocking out seeds, let’s try.”
Portugal’s Jose De Sousa sparked an afternoon of comebacks and upsets in north London by overturning a 3-0 deficit to defeat Ryan Searle 4-3.