Both produced classy performances to progress into the last 32 of the £1 million tournament on Monday evening.
Webster was particularly impressive in his 3-1 success over Ian White.
The Welshman hit seven 180s and posted a fantastic average of 97 to dispatch of one of the most dangerous unseeded players in the tournament.
“I knew I was in for a tough game,” said Webster, who faces Colin Lloyd or Darin Young in round two.
“I can take a lot of positives out of that win and I’m really looking forward to the next round.
“I showed what I can do again and I’m really up for this tournament. It is massive and I’m pleased with my performance tonight.”
Wade made light work of a potentially tricky opponent in Peter Hudson.
‘The Machine’ put together a solid display to see off ‘The Rock’ in straight sets.
He said: “I’ve been working very hard but I wasn’t at my best tonight.
“I’m pleased because I have beaten a good player but there is much better to come from me.”
Arron Monk was unable to join Wade and Webster in the last 32. The former World Youth Champion was defeated by Peter Wright.
By Chris Murphy
Images courtesy of Lawrence Lustig/PDC