Michael van Gerwen and James Wade also progressed on day two in Blackpool, where the opening round continued with eight matches.
Anderson averaged 109.96 in a 10-2 win over Joyce, the eighth-highest average ever recorded in the World Matchplay.
The Scottish number one was in complete control throughout, rounding off his display with successive 144 and 141 finishes.
"You get those days sometimes where you can throw with your eyes shut and hit everything and today was one of those days," Anderson said.
"I've missed a lot of tournaments this year. I play when I can, and I came here not knowing what to expect.
"The next game will be a completely different game, so we'll see what happens."
His reward is a second-round meeting with Jonny Clayton, who beat Australia's Damon Heta 10-7.
Clayton looked set for a comfortable victory after moving 8-3 ahead before Heta threatened a comeback. The Welshman eventually sealed the win with a 144 checkout.
"I loved every second of that," Clayton said.
"This is the best venue in darts, and I'm a proud man to be standing here with a win to my name.
"Gary Anderson was my hero in darts. I think it's going to be a battle of the old boys, but I hope it's going to be a belter."
Van Gerwen also came from behind to reach the last 16, recovering from 4-1 down to defeat Andrew Gilding 10-6.
The Dutchman narrowly missed double 12 for a nine-dart finish in the sixth leg before taking control of the contest, winning nine of the final 11 legs to book a meeting with compatriot Dirk van Duijvenbode.
"It was a strange game," Van Gerwen said.
"I think I had some really good patches and some really poor patches, but when you win the game, that's the most important thing.
"This was a good win for myself. There is still a lot more in the tank, and I hope I can show that later in the tournament."
Van Duijvenbode survived four match darts to edge past Chris Dobey in a deciding tie-break, despite the Englishman hitting 13 maximums.
It completed an impressive day for the Dutch contingent, with Gian van Veen and Wessel Nijman also advancing.
Van Veen overcame Krzysztof Ratajski in a ruthless display that featured two 144 checkouts and a 160 finish, converting 67% of his double attempts.
Nijman, who has won eight ranking titles this year, averaged just under 99 in a comfortable win over Dave Chisnall.
The pair of Dutch winners will now meet in the second round on Wednesday.
Elsewhere, 2007 champion Wade began his 21st consecutive World Matchplay campaign with a 10-7 triumph over Jermaine Wattimena.
Ryan Searle also progressed after beating William O'Connor 10-7, landing 56% of his doubles to overcome the Irish number one.
Wade and Searle will now meet for a place in the quarter-finals.
The opening round concludes on Monday evening, with defending champion Luke Humphries beginning his campaign against Cameron Menzies, Rob Cross facing Danny Noppert, Gerwyn Price taking on Martin Schindler and Ross Smith meeting Kevin Doets.
Sunday's results
Dirk van Duijvenbode 13-11 Chris Dobey
Gary Anderson 10-2 Ryan Joyce
Michael van Gerwen 10-6 Andrew Gilding
Jonny Clayton 10-7 Damon Heta
Ryan Searle 10-6 William O’Connor
James Wade 10-7 Jermaine Wattimena
Gian van Veen 10-6 Krzysztof Ratajski
Wessel Nijman 10-5 Dave Chisnall