The duo, who hail from Delhi, emerged victorious after answering all the 14 questions correctly with the help of four lifelines.
"There was a mission in the manner in which they approached the game. Right from the very start, they went about it in a manner that was simply exemplary. They used up all their lifelines, but they had the answer even before they asked for help," the 71-year-old actor posted on his blog.
"What a joy to see a 28-year-old and his younger brother of 23, playing to gather some money to be able to put it into the cause of providing the fees required for the treatment of their mother who suffers from ovarian cancer.
"Achin and Sarthak Narula, you deserve not just the highest reward of the show but indeed all the wishes for propagating this important message that if an ailment is brought to the notice of the medics in correct time, the possibility of a cure and its success is possible," Bachchan added.