It took the hosts 79 minutes to finally break the deadlock, striker Wuttichai Tathong breaching the Songkhla defence to open the scoring.
And the points were wrapped up in the third minute of added time as Serbian forward Milan Bubalo found the net.
Sunday's victory sees Muang Thong stay at the summit by three points after they had been temporarily displaced courtesy of Buriram United's 3-1 triumph against Bangkok Glass a day earlier.
Buriram now sit second, leapfrogging BEC Tero Sasana, who slipped to a 1-0 defeat at Chonburi, a second-half penalty from Thiago Cunha settling the encounter.
Meanwhile, Bangkok United went seven points clear of the drop zone with a fifth straight success in all competitions, beating Singhtarua 3-0 away from home.
Police United also dropped down the standings as a result of Sisaket's win and are dangerously close to the relegation places after losing 1-0 at Army United.
