The Welshman nicknamed ‘Spider’ proved to be deadly on his doubles as clinical finishing earned him a 10-6 victory against the world number two.
The former Lakeside World Champion continued his recent revival to set up a last eight clash with Raymond van Barneveld.
“I’m really pleased, I did a professional job and I’m over the moon,” said Webster, who reached the semi-finals of the World Grand Prix last month. “I knew I had to do something out of the ordinary – I wasn’t going to have a 108 average so I had to finish well and take my chances and I did that.
“Gary still averaged 103 but he didn’t play like he can, and I’ve beaten all the top players when they don’t bring their A-game. I can compete with their B-game and I’ve done it again tonight.
“Once I got a lead I defended that lead very well and I’m pleased. I can play a lot better than that, but I got the job done so I’m happy.
“It’s a massive scalp, he’s the World Champion and a good player and I knew I had to finish well to beat him.”
Webster landed early finishes of 92, 80 and 96 to put himself 3-1 ahead and he later took out 127 on the bull to lead 6-2.
A 108 checkout soon followed as Webster continued to hold his throw and his nerve to secure a fabulous victory.
He will face van Barneveld on Friday for a place in the last four.