Bryan Ruíz, farmed out on loan by relegated Fulham midway through last season, decided the outcome with a first-half header to seal Roy Hodgson's squad's fate and send Costa Rica to the top of Group D.
The Costa Ricans' victory - six days after their 3-1 defat of Uruguay - marks their first progression to the last 16 since Italia '90.
A nation of 4.8 million, their coach Jorge Luis Pinto said before the tournament "The braver the bull, the braver the bullfighter," and Costa Rica's triumph is one of the great modern World Cup stories.
Premier League cast-offs have punished England before at tournaments, but unlike Viorel Moldovan in 2000, Niclas Alexandersson in 2002 and Hélder Postiga in 2004, Ruíz indirectly did the damage.
Football Association chairman Greg Dyke has already said Hodgson will be in charge for England at the 2016 European Championship, but elimination before half the competition's teams have played their second game signals an abject failure.