The duo had started the day trailing overnight leader Felipe Aguilar by two and three shots respectively but enjoyed a productive run on the front nine to take the lead.
Singh had been making par along the first five holes but his turning point came on the par-five sixth when he sent his approach shot to within six feet of the pin before comfortably sinking the putt for an eagle.
He then added a birdie two holes later on the short eighth when his tee shot landed seven feet from the pin and he made the putt to move ahead on the leaderboard.
Thai Meesawat, meanwhile sank three successive birdies from the fifth before adding another on the ninth to move on to 17 under overall at the turn, a stroke ahead of James Kamte and Aguilar.
South African Kamte, hoping to record his first victory on the European Tour at the Cengkareng Golf Club, picked up shots on the first and second holes before adding another birdie on the sixth, which saw him briefly move top of the leaderboard.
However, a bogey on the par-three eighth saw him drop back down to 15-under-par before he birdied the ninth and was 16 under overall through nine.
Chilean Aguilar, who was the overnight leader at the end of the second and third rounds, will need to pick up the pace on the back nine if he is to secure a maiden European Tour victory.
The 33-year-old bogeyed on the second before picking up a shot on the ninth to reach the turn at level par.
Englishman Philip Golding was making fine progress in his attempt for a second European Tour title. The Luton-born 45-year-old picked up four birdies in a faultless run on the front nine and trails Singh and Meesawat by just three strokes.
Topics : Golf