The Consadole Sapporo midfielder's second-half strike was golden for the Thais, who had seemed in disarray when they sacked their coach Milovan Rajevac after opening with a 4-1 loss to India.
It improved the War Elephants' record to two wins from 22 Asian Cup games and left them temporarily second in Group A behind India, who play hosts the United Arab Emirates later.
Thailand had zero shots on target as Bahrain controlled the first half, with Mohamed Jasim Marhoon and Sayed Dhiya Saeed coming closest as they forced goalkeeper Chatchai Bootprom into a sharp double save.
But bleach-blond Chanathip, whose fans compare him to Lionel Messi, put the Thais in the driving seat near the hour-mark with a superbly struck first-time shot that rocketed past Sayed Shubbar Alawi in the Bahrain goal.
Chatchai saved brilliantly from Ali Jaafar Madan's snap-shot as Bahrain hunted for the equaliser, while Adisak Kraisorn, fed by Chanathip, belted one off the post at the other end.
Thailand's only previous Asian Cup win was in 2007, when they co-hosted the tournament.