But Parks silenced their celebrations when he was allowed to skip through the Japan defence before scoring with a fierce shot from close range.
Moments later Akinori Nishizawa almost restored Japan's lead only to see his glancing header come back off the post after a superb cross from Brazilian-born midfielder Alessandro Santos.
In only his second match for his adopted country, Santos wreaked havoc on the left flank, creating numerous chances for his attackers and it was their profligacy which ultimately cost Japan the game.
Kashima Antlers striker Takayuki Suzuki was the chief culprit, missing the target with three close-range headers in quick succession after the interval.
Japan's coach, Philippe Troussier, said he was satisfied with the result.
"Our players showed a lot of toughness both mentally and
physically," he said.
Costa Rica, missing Paulo Wanchope, Hernan Medford and Reinaldo Parks, will look to build on this performance in their next match in the Far East against South Korea on 20 April.
Japan, who co-host the World Cup with South Korea, play Belgium, Russia and Tunisia in World Cup Group H.
Costa Rica will face Brazil, China and Turkey in Group C.
Japan: Seigo Narazaki; Tsuneyasu Miyamoto (Shunsuke
Nakamura 82), Naoki Matsuda, Koji Nakata, Alessandro
Santos (Toshihiro Hattori 80), Kazuyuki Toda, Tomokazu
Myojin (Yasuhiro Hato 81), Mitsuo Ogasawara (Hiroaki
Morishima 26), Daisuke Ichikawa (Takashi Fukunishi 46),
Takayuki Suzuki (Tatsuhiko Kubo 87), Atsushi Yanagisawa
(Akinori Nishizawa 30)
Costa Rica: Erick Lonnis; Mauricio Wright, Luis
Marin (Alexander Madrigal 46), Harold Wallace (Daniel
Vallejos 77), Gilberto Martinez, Wilmer Lopez (Oscar
Rojas 68), Mauricio Solis, Walter Centeno (Max Sanchez
77), Juan Jose Rodriguez, Ronald Gomez (Steven Bryce
84), Rolando Fonseca (Winston Parks 68)
Referee: Huang Junjie (China).