Wade, looking for his first World Championship crown, won the first two sets, dropping just one leg to his opponent, and establish total command.
Farmer missed one dart to claim both the third and fourth sets, allowing Wade secure a comfortable and set up a mouth-watering clash against John Part.
"It wasn't as easy as the scoreline suggests," said Wade, whose best performance in this tournament is a semi-final appearance back in 2009.
"I feel fine and I'll just keep playing the way I have been. I've only lost one set in three matches so far, so I must be doing something right!
"I'm looking forward to playing John on Friday. We had an epic quarter-final here back in 2008, which he won. I would to get back over him this time around."
Wade, seeded three for this year's event, hit double five to take the first leg of the game and defied a maximum from Farmer to win the second on double top.
Wade, who defeated Jelle Klaasen in the previous round, fired a 180 of his own in the third leg and won the set by landing double 10 with his first dart, to establish an early advantage.
Farmer won his first leg of the game at the start of the set two, before Wade hit double nine to the second, and then won the third by taking out 70, in two-darts.
The fourth leg saw Farmer off-target with a dart at double top for a 107 finish, and Wade hit double 10 to take the set and lead 2-0.
Farmer, who defeated Kevin Munch to reach this stage, capitalised on missed doubles from Wade to take the opening leg of the third set.
The man from Shropshire then hit double eight to win the second against the darts, before Wade took the third by landing double top.
Farmer missed a dart at double 18 to win the set in the next leg, which proved crucial as the UK Open Champion hit tops and then hit double two with his last dart in the fifth leg to move three sets clear.
Farmer, making his second appearance at Alexandra Palace, held throw at the start of the fourth set and then broke throw after Wade was guilty of missing eight darts at doubles.
Wade hit back from that disappointment to take the third leg with a 14-dart finish and then won the fourth in 12-darts to move a leg away from victory.
The fifth leg saw Farmer miss a dart at bullseye for a 132 checkout and Wade hit a clinical 116 checkout to seal a last eight spot.
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