Fowler scored the equaliser for his side after Songkhla had taken the lead inside two minutes through Malek Yawatab.
Diyara Ali then put Muang Thong ahead before Boubah Kwadwo equalised to force the semi-final into extra-time. Neither side was able to break the deadlock in the additional 30 minutes which meant penalties were needed to decide the finalist.
Fowler's charges (the Englishman is player-coach of Muang Thong) ultimately prevailed 6-5 to set up a summit clash with Thai Premier League champions Buriram PEA, who beat Army United 2-0 at the Rajamangala National Stadium thanks to first-half goals from Suchao Natnum and Frank Acheampong.
The two sides will meet in the final on January 10.
For Buriram, a victory would mean they'd be in with a shot of completing a historic treble, since they've also qualified for the final of the Thai League Cup in which they'll play Port FC in February.