Englishman Wade had apologised for controversial post-match comments that he "wanted to really hurt" Japanese opponent Seigo Asada after his previous victory at the Alexandra Palace, blaming his actions on a "hypomanic episode".
Despite enduring a hostile reception from large sections of the crowd and having found himself facing another stern test as Brown moved into a 3-1 lead, there was no repeat of any such outburst.
Wade eventually found his range to take the fifth set 3-0 and went on to progress in the decider against the player who had ended his world title hopes last year.
The 35-year-old from Aldershot will face the impressive Ryan Joyce for a quarter-final place.
Mervyn King was, though, another of the seeds to fall in round three, beaten 4-2 by Northern Ireland's Brendan Dolan.
The number-19 seed, twice a semi-finalist, had battled back to level the match at 2-2 following a 14-dart finish.
However, Dolan responded to break King and take the fifth set on a decider before closing out victory with a 95.73 average, reaching the last 16 for the first time.
Dolan, who saw off 14th seed Joe Cullen in round two, will play either Benito Van De Pas or Toni Alcinas for a place in the last eight.
In Sunday's early match, Chris Dobey battled through 4-3 against Vincent Van der Voort.
After the first four sets went with throw, Dutchman Van der Voort broke twice to lead 3-2.
However, Englishman Dobey recovered with a flawless set to force a decider, and progressed with a 97.87 average to set up a fourth-round match against number-four seed Gary Anderson.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies