The 28-year-old former captain, who had not represented his country since February 2013, smashed home a clinical volley after 18 minutes.
Greece, who laboured for long spells, failed to capitalise on a spell of first-half pressure which saw them hit the woodwork three times and Fernando Santos's team were punished when Son Heung-Min made it 2-0 after 55 minutes.
The first chance fell to Korea in the seventh minute when Park played a clever through ball for Lee Chung-Yong and his shot was saved brilliantly by Panagiotis Glykos as he blocked the ball with his legs.
The visitors continued to look the most dangerous team and Park finished emphatically after peeling away from the Greece defence and latching on to a superb chip from Koo Ja-Cheol.
Kostas Katsouranis missed a good chance to level in the 23rd minute when he hit the post with only the keeper to beat.
The hosts were again unlucky on the half-hour when Vassilis Torosidis headed against the bar and Avraam Papadopoulos did the same from the rebound.
Park, who featured at the 2006 and 2010 World Cups and recently joined English second-tier team Watford on loan from Arsenal in a bid for more playing time, was impressive throughout.
Korea have been drawn in Group H with Belgium, Algeria and Russia at the World Cup in Brazil in June.