Is there an English equivalent to this familiar saying used in India:
Don't speak unless you can improve silence.
The saying loosely means it is better to be silent than prattle on about something.
Let not thy tongue run away with your brains
I'm not sure whether it is of English origin, but it has been around for a while, since it can be found in:
Gnomologia: Adagies and Proverbs; Wise Sentences and Witty Sayings, Ancient and Modern, Foreign and British collected by Thomas Fuller; B. Barker ... and A. Bettesworth and C. Hitch, 1732
A modern version can also be found (on-line at least):
Let not your tongue run away with your brains.