The Flying Scotsman is chasing a third world crown after title wins in 2015 and 2016.
The Flying Scotsman changed his glasses and darts after struggling to find his best form in the early rounds at Alexandra Palace.
Anderson’s tactic worked as he hit seven 180s and averaged 97.27 to beat Rob Cross 4-3 and reach his seventh world championship quarter-final in eight years.
“I went back to the old darts and they were working a treat,” Anderson, world champion in 2015 and 2016, told Sky Sports.
“I was doing all right. I was 3-1 up and made a complete mess of one leg.
“Rob stuck in and came back. But there were no nerves.
“I win and it’s fantastic to get through. If I get beat I go home and spend a few extra days with the family. No pressure whatsoever.”
Cross, the 2018 world champion, claimed the first set but Anderson then won five successive legs and a 170 checkout helped him into a commanding 3-1 lead.
Anderson missed seven darts at a double for a 2-0 lead in the fifth set, and Cross – who produced a 144 checkout – stormed back to level proceedings in what was fast becoming an Ally Pally thriller.
But Anderson kept his nerve and dominated the last set to secure a quarter-final tie with Luke Humphries.
Peter Wright took out Ryan Searle 4-1 with the Scot’s scoring power – the 2020 world champion hit seven 180s and 20 140s – too much for his English rival.
The pair met in the decider of the Players Championship Finals last month, which Wright edged 11-10.
But it was far more straightforward for Wright this time with his third-set average of 102 ending Searle’s hopes of mounting a comeback.
James Wade will meet Mervyn King in the last eight after coasting to a 4-0 win over Martijn Kleermaker.
The Dutchman won only four legs as Wade moved to within one victory of a fourth World Championship semi-final appearance.
Wade said: “This game is so nice and so enjoyable when you’re hitting the odd shot here and there.
“When you’re not hitting it then it’s the most boring thing in the world. I’m just grateful to be picking and nicking little shots off there.”
In the afternoon session, King and Humphries both recovered from 3-1 deficits to claim respective 4-3 victories over Raymond Smith and Chris Dobey.
Callan Rydz reached the last eight with a 4-1 victory over Alan Soutar.
Rydz recovered from losing his first set of the tournament to make the quarter-finals for the first time.