Webster, who famously defeated Taylor at Alexandra Palace in 2011, triumphed by three sets to one against Dutch youngster Meulenkamp.
The former Lakeside World Champion will take on Taylor on December 28 and is looking forward to the prospect.
He said: “Playing the best ever player represents an opportunity to beat him. I’ve done it before and it’s what I want to do again.
“Today’s performance wasn’t pretty but it was the performance of a man who hasn’t played on TV for a year.
“I played well to start with but it got a bit messy by the end. But when you’ve not been winning it doesn’t matter about stats and averages, it’s just about getting the win.
“I’ve done that now and I’ll come back after Christmas looking forward to playing Phil.”
Two 180s and clinical finishing saw Webster take the first set by three legs to one, with the Welshman not missing a dart at a double as he took out 104, 45 and 107 after losing the opening leg.
Another two maximums helped him double his lead as he edged the second set 3-2, before Meulenkamp took the third to keep his hopes alive.
Webster wrapped the win up in a scrappy final set, in which many a double deserted both players, taking it by three legs to one.