Having been thrashed 4-1 by India in its opening Group A fixture, Thailand promptly sacked head coach Milovan Rajevac and placed Sirisak Yodyadthai in temporary charge.
And it bounced back in style at Al Maktoum Stadium as Songkrasin's well-taken effort shortly before the hour reignited its campaign and secured just a second win in 22 matches in the competition.
Bahrain, which has just a point to show from its two outings after Sunday's (AEDT) 1-1 draw with host United Arab Emirates, had the better of a dour first half and perhaps could have been awarded a penalty when Teerasil Dangda appeared to block Sayed Dhiya Saeed's free-kick with his arm.
Mohamed Al Romaihi wastefully headed over at close range from Mohamed Marhoon's delivery shortly before the interval - a miss Bahrain were made to regret.
Tristan Do was superbly released down the right by Adisak Kraisorn and his deflected cross fell perfectly for Songkrasin to smash home from 10 yards.
Thailand goalkeeper Sivarak Tedsungnoen saved brilliantly from Ali Jaafar Madan inside the six-yard box to preserve his side's lead soon afterwards.
That advantage was almost extended 18 minutes from time as Songkrasin played in Kraisorn, who struck the base of the post, but it mattered little as Thailand held on to give their chances of reaching the last 16 a huge boost.