Chopra scored either side of a left-foot Lee Martin strike to send Ipswich to the top of the table on goal difference.
The former Cardiff player first lobbed the ball over David James following a Mark Kennedy pass on 13 minutes.
Fifteen minutes after the break, Chopra dispossessed the former England keeper after a short backpass and knocked the ball into an empty net.
Both sides have home Carling Cup encounters on Tuesday. Bristol face Swindon and Ipswich take on Northampton.