Chopra was next to go close for Ipswich, but his effort was off target when he might have done better.
Lee Bowyer had a golden chance for the home side after 26 minutes, but his strike was wide of the target.
Emmanuel-Thomas came close for Ipswich moments into the second period, but fired his effort wide with the Tractor Boys in complete control.
Ipswich eventually took the lead after 54 minutes when Chopra fired a Martin cross into the back of the net.
David Edgar had the away side's best chance of the match after 70 minutes, but he fired wide from inside the box.
The home side lost Leadbitter to a red card late on, but they held on for all three points.
Ipswich have moved into 14th in the Championship table, while Burnley drop to 16th.