Ecuador booked a place in the knock-out stages for the first time ever with a comfortable win which also put Germany through to the second round.
Ecuador goalscorers Delgado and Tenorio celebrate
Carlos Tenorio gave Ecuador an eighth-minute lead with a powerful header from Luis Valencia's cross.
The advantage was doubled when Agustin Delgado lashed home from a tight angle shortly after half-time.
Ecuador finished with a flourish when Ivan Kaviedes capped a flowing move by volleying home from six yards.
Knowing defeat would end their hopes of reaching the second round, Costa Rica could not have made a worse start as they fell behind after just eight minutes.
Delgado's shot was charged down, but the rebound fell kindly, allowing him to feed Valencia whose whipped cross was powerfully headed home by Carlos Tenorio.
Segundo Castillo then tested Costa Rica keeper Jose Porras from a free-kick which earned Luis Marin a yellow card for his foul on Carlos Tenorio.
Much of the football was pretty but with no real purpose as Ecuador formed around the imposing central pairing of Ivan Hurtado and Geovanny Espinoza and allowed Costa Rica to pass the ball square in front of them.
It took Costa Rica 39 minutes to muster their first on-target shot, with Mauricio Solis firing straight into Cristian Mora's midriff from 25 yards.
At the other end, Porras reacted brilliantly as Valencia's cross deflected goalwards off Marin.
Costa Rica opened Ecuador up for the first time but Douglas Sequeira's free header was disappointing after Leonardo Gonzalez's cross picked him out at the far post.
Costa Rica needed a sharper cutting edge to stay alive in the competition but former Premiership striker Paolo Wanchope was a disappointment.
Los Ticos were facing a mountain to climb when another former Premiership striker, Delgado, doubled Ecuador's lead.
Delgado drilled home at the near post
Kaviedes flicked the ball inside where Delgado, once of Southampton, chested it down to lash a ferocious shot inside Porras's near post.
Ecuador keeper Mora was at last called into action, palming away a stinging effort from Solis.
Costa Rica were denied a goal which might sparked a late rally when Alvaro Saborio curled a shot against the bar.
Ecuador scored a third when former Crystal Palace striker Kaviedes rounded off a flowing move by volleying home Edison Mendez's cross.
For a team that took 35 years to win an international outside their high-altitude capital Quito, Ecuador showed they will be no pushovers.
With a superior goal difference, a draw in their final game against hosts Germany will see Ecuador top their group.
Ecuador: Mora, De la Cruz, Reasco, Espinoza (Guagua 68), Hurtado, Castillo, Valencia (Urrutia 73), Edwin Tenorio, Mendez, Carlos Tenorio (Kaviedes 45), Delgado.
Subs Not Used: Villafuerte, Perlaza, Lara, Borja, Ambrossi, Ayovi, Saritama, Lanza, Benitez.
Booked: Castillo, De la Cruz, Mora.
Goals: Carlos Tenorio 8, Delgado 54, Kaviedes 90.
Costa Rica: Porras, Gonzalez (Hernandez 56), Umana, Wallace, Marin, Fonseca (Saborio 28), Centeno (Bernard 84), Solis, Sequeira, Wanchope, Gomez.
Subs Not Used: Drummond, Bolanos, Azofeifa, Badilla, Nunez, Rodriguez, Alfaro, Mesen.
Booked: Marin, Solis.
Referee: Coffi Codjia (Benin).
Fifa man of the match: Agustin Delgado
Ecuador have reached the last 16 of the World Cup for the first time and will win Group A if they draw with Germany or beat them. On their debut in 2002, Ecuador finished fourth in a group with Mexico, Italy and Croatia. Germany are also through to the next round, because of Ecuador's result.
This 3-0 win over Costa Rica is Ecuador's biggest World Cup victory. Agustin Delgado remained sole top scorer for his country after netting his third World Cup goal. Ivan Kaviedes became only the fourth Ecuador player to score in the World Cup finals, joining Delgado, Edison Mendez and Carlos Tenorio.
Costa Rica fielded their oldest ever starting line-up at the World Cup. Their average age was 29 years and 351 days. By playing against Ecuador, Harold Wallace joined Luis Marin, Gilberto Martinez, Mauricio Solis, Walter Centeno, Paulo Wanchope, Ronald Gomez (2002, 2006) and Hernan Medford (1990, 2002) as the eighth Costa Rican with two World Cup participations.