The 32-year-old former BDO world champion from Denbigh won 4-0, and was never in trouble.
He faces Alan Norris for a quarter-final place on Wednesday, 30 December.
"I settled in ahead of him and pinching the second set clinched it for me, it was a long way back for him then and I didn't have to do anything special," said Webster.
PDC darts results and draw
"I just played steady and I took my chances and basically that's what I do, and I'm pleased with that.
"I think back to 18 months ago and I was distraught.
"I was losing to players that I didn't think I'd lose to.
"I wasn't doing myself justice, my technique had gone. I've worked hard, my technique still isn't great, but I'm making it work for me at the minute."
Wales' Mark Webster dominated England's World No 11 Terry Jenkins to reach the last 16 of the PDC World Championship.