Wright, 54, averaged just 89.63 compared to his opponent’s 93.77, but he did enough to make progress.
Crowd favorite ‘Snakebite’, sporting a purple mohawk and formal attire, showed flashes of his best form as he won the first set and survived eight sets of darts to take a 2-0 lead.
He lost the next one, but Dutchman Plaisier missed two more darts in the fourth and Wright took his chance.
“Wesley had his chances but he blew them and I took them,” he said. “He has his tour card and next year he will be a dangerous player for all the players playing against him.”
Sherrock (30) defeated her English compatriot Meikle, losing 2-1.
She then narrowly missed the bull and smashed 170 in the fourth over before the left-handed Meikle controlled her nerves and hit a double of 18 to finish with 96 to seal a hard-fought success.
“I felt pressure from the very beginning and it was unbelievable to experience it,” Meikle said.
“It’s an incredible reward to play Luke here on this stage. This is the biggest stage of all. I’m very happy.”
World number 81 Jeffrey de Graaf, born in the Netherlands but currently representing Sweden, had trouble with Rashad Sweeting before winning 3-1.
Sweeting, who made history as the first Bahamian player to compete in the tournament, won the first set, but De Graaf fought back to set up a second-round meeting with two-time champion Gary Anderson
German Ricardo Pietreczko, ranked 34th, defeated China’s Xiaochen Zong 3-1 and will next face Gian van Veen.