Lookman put the ball into the net from Jonjoe Kenny's low drilled cross to open the scoring in the 35th minute of the game. England continued to dominate the game and doubled the lead through Lookman in the 63rd minute.
Arsenal youngster Ainsley Maitland-Niles handled the ball in the box to award an 89th-minute penalty to Costa Rica. Newcastle United keeper Freddie Woodman managed to save the initial effort from Randall Leal, but couldn't keep the rebound out.
The Young Lions, who have qualified to the last-8 for the first time since 1993, will play either of Mexico or Senegal in the quarter-finals.