"The crowd got me through that whole match," Wright admitted in his post-match press conference.
"The support did spur me on. I didn't want to let them down, I didn't want to let my family down, and thankfully I got away with it tonight.
"It's nice to see Jermaine (Wattimena) playing some fantastic darts, so I’ve got to step up, but class is permanent, and form is temporary."
Wright will now face Wattimena, who defeated James Wade earlier in the tournament.
Wright took an early lead, capitalising on missed opportunities from Plaisier to go up two sets. However, Plaisier fought back, winning the third set with a 136 checkout. Wright then rallied to win the fourth set and secure his place in the last 32.
In a surprise result, World Grand Prix champion Mike De Decker became the second seed to be eliminated, losing 3-1 to Luke Woodhouse. Woodhouse, a European Championship semi-finalist, capitalised on a subpar performance from De Decker.
"It wasn't an Ally Pally classic by any means, but to be in the last 32 is unbelievable," Woodhouse said. He will face either Connor Scutt or Damon Heta in the next round.
Ryan Meikle ended Fallon Sherrock's hopes of another historic run with a deciding-set victory. Meikle hit three ton-plus checkouts (111, 119, and 122) and sealed the win with a 12-dart break. He will now face Luke Littler.
Noa-Lynn van Leuven's World Championship debut ended with a 3-1 loss to fellow Dutchman Kevin Doets, who will now face Michael Smith. Jeffrey de Graaf recovered from a scare to defeat Rashad Sweeting, the first player from the Bahamas to compete in the tournament.
Sweeting nearly took a 2-0 lead but ultimately fell to de Graaf, who will face Gary Anderson in the next round.
Other results included Ricardo Pietreczko's straight-sets victory over Xiaochen Zong, setting up a match against Gian van Veen. Ryan Joyce continued his strong form with a win over Darius Labanauskas and will play Danny Noppert.
James Hurrell made a successful debut with a straight-sets win over Jim Long, earning a match against Michael van Gerwen.