Burnley were back in front before half-time after Cork headed in from close range.
Foden equalised for a second time through Sergio Aguero only to fall behind again with Cork scoring his second with a left-footed drive.
A fine Jay Rodriguez finish made it 4-2 and a second for Aguero came too late as Foden bowed out of the competition.
Taylor joked after the match that he has never seen Cork score a double before.
“I have seen him score plenty of goals, but never two in a match," the left-back said.
James Maddison (LEI) 8-1 Callum Wilson (BOU) | Report and highlights
Max Aarons (NOR) 4-1 Ryan Sessegnon (TOT) | Report and highlights
Phil Foden (MCI) 3-4 Charlie Taylor (BUR)
John Egan (SHU) 4-3 Jofra Archer (MUN) | Report and highlights
James Maddison (LEI) 3-2 Max Meyer (CRY) | Report and highlights
Finals Day will also be shown live in the UK on Sky Sports' Premier League and Main Event channels, with the tournament again being televised around the world by the Premier League's international broadcast partners.
The tournament will urge everyone to follow official advice by staying at home and saving lives.
We would also ask anyone inspired to play FIFA 20 to take regular breaks from gaming, every 45 minutes.