Bhullar, who shot 71 on first day to lie 18th, was six-over through 10 holes for the second round and looked certain to make an early exit.
But he hauled himself back with an eagle on 12th and birdies on 15th and 17th for a round of 74 and at one-over 145 he was tied 26th, down eight places. Bhullar had six bogeys in first 10 holes.
However, Jeev Milkha Singh's wretched run continued as he carded an error-filled 78 and crashed out at five-over 149. Jeev stumbled to seven bogeys and just one birdie.
The 22-year-old who made the main Tour through the school at this very venue overcame three bogeys in his first four holes to record a second consecutive 69.
Pieters, who was eighth in Malaysia last month, is now six-under, one ahead of first round leader Eddie Pepperell and Dutchman Joost Luiten.