Gowda, who won the Glasgow Commonwealth Games gold, achieved a best throw of 62.58 metres in his second attempt, out of six, which was enough to secure the second spot.
However, the attempt was below his bronze-medal winning mark of 63.13m at the 2010 Guangzhou Games.
The 31-year-old Mysore-born managed 59.52m in his first attempt before achieving 62.58m in his second and 60.77m in his third throw. However, his last three attempts were disqualified.
Gowda took the lead among 14 competitors after the first throw but was overtaken after the second throw by gold-medal winner Ehsan Hadadi of Iran, who claimed the yellow metal with 65.11m.
This was Hadadi's third straight Games gold after throwing 63.79m in 2006 Doha and 67.99m in 2010 Guangzhou.
Qatar's Mohammed Ahmed Dheeb clinched bronze with a best throw of 61.25m in his final attempt.