Relegation-threatened Augsburg leveled the scores in the 23rd minute through Koo Ja-cheol, but Gomez was on hand for his second of the afternoon latching onto a pass from Dutch winger Arjen Robben in the 59th minute to claim his 25th goal of the season.
South Korea, victors the first two times the tournament was held in 1956 and 1960, took the lead in the 24th minute at Doha's Al Gharafa Stadium through Koo Ja-cheol.