Following their shock win over Germany, Japan were frustrated by a tight defensive unit, before Fuller struck with Costa Rica’s first shot on target at the tournament.
The result leaves both teams on three points after two games, with Spain – who still top the group on goal difference – facing Germany later on Sunday (19:00 GMT).
Victory for Spain will all but guarantee their progression to the last 16.
After beating Germany in their opener, many expected Japan to account for a Costa Rica side reeling from a 7-0 thrashing by Spain.
However, Japan boss Hajime Moriyasu opted for rotation over continuity, making five changes, and that resulted in a subdued performance and a scoreline that blew the group wide open.
It was a remarkable victory for Costa Rica, who had failed to lay a glove on the Japan defence before Fuller’s deflected shot from the edge of the box escaped goalkeeper Shuichi Gonda’s grasp nine minutes from time.
After a first half devoid of goalmouth action in the searing heat at Ahmad Bin Ali Stadium, Japan dominated for large spells.
However, they struggled to create clear-cut chances until the 88th minute, when Daichi Kamada could not turn the ball home after a driving Kaoru Mitoma run.
Having achieved redemption following their humiliation at the hands of Spain, the Costa Rica players celebrated emotionally at full-time as Japan were left to rue a disappointing display that failed to back up their heroics against Germany.
