World number one Michael van Gerwen also reached the quarter-finals and Dimitri van den Bergh upset Raymond van Barneveld on a scintillating evening at the Braehead Arena in Glasgow.
Number one seed Anderson averaged 103.57 as he defeated Chris Dobey, a player he helps to mentor, 6-1.
Finishes of 130 and 110 were the highlights as Anderson booked a quarter-final clash with Gerwyn Price, who overcame Corey Cadby 6-5 in a fiery encounter.
The world number 18 averaged 93.86 to set up the sixth meeting between himself and two-time world champion Anderson, with the Scot currently leading the head-to-head 3-2.
The pair last met in a Players Championship event in March 2016, where Anderson came out a 6-0 winner and the 46-year-old is looking forward to another clash with the Welshman.
"Bring it on," he said.
"I just want to get up on stage and play darts, if he wants to give it that’s entirely up to him but I’m going up to play my darts, and hopefully play well," added Anderson.
Wright also delighted the Scottish crowd and will face Daryl Gurney for the 16th time on Sunday afternoon after defeating Justin Pipe 6-1.
The world number two is still aiming to secure the title in Glasgow but believes he will have to improve if he is to beat the Northern Irishman.
"I did enough tonight. It’s tough playing Justin because he is such a good friend but there is obviously more to come," said Wright after his match.
"Daryl beat me last weekend so it will be nice to play him again and hopefully get a little bit of revenge."
Gurney defeated Simon Whitlock 6-3 with an average of 103.64 in a repeat of last month's World Grand Prix final.
World Champion van Gerwen kept his hopes of a third consecutive World Series Finals crown alive and moved safely in to the last eight after a comprehensive 6-1 win over Max Hopp.
The 2017 Shanghai and Las Vegas Masters Champion averaged 102.98 and will face Rob Cross in the quarter-finals after he survived a late comeback to beat the Auckland Masters champion Kyle Anderson 6-5.
Van den Bergh averaged 102 and hit five 180s as he knocked out van Barneveld to move in to the first televised quarter-final of his career.
The 23-year-old will now face James Wade in the next round. Wade was a 6-5 winner over Simon Stevenson.
Second-round results
- James Wade (5) 6-5 Simon Stevenson
- Raymond van Barneveld (4) 4-6 Dimitri Van den Bergh
- Gerwyn Price (8) 6-5 Corey Cadby
- Gary Anderson (1) 6-1 Chris Dobey
- Peter Wright (3) 6-1 Justin Pipe
- Michael van Gerwen (2) 6-1 Max Hopp
- Daryl Gurney (6) 6-3 Simon Whitlock
- Kyle Anderson (7) 5-6 Rob Cross
Related links
Fast Results
Scores
Racecards 
