Chopra headed the home side in front midway through the first half, converting Lee Martin's cross from six yards out under little pressure from the City defence.
And after the break the visitors were punished once more, as Tommy Smith nodded Andy Drury's corner beyond David James in the Robins' goal.
Smith then rattled the crossbar before Andy Drury added some extra gloss by smashing in a long-range third.
City's afternoon was made that little bit worse by injury to Albert Adomah, as the West Country side slipped to their sixth straight defeat on the road in all competitions.
The visitors created little over the course of the 90 minutes, with Liam Fontaine and Adomah producing decent saves out of Alex McCarthy in the Ipswich goal, but left Portman Road without anything to show for their efforts.
The hosts made two changes for the clash. McCarthy returned in goal in place of Arran Lee-Barrett and Grant Leadbitter was handed a place in midfield, as Luke Hyam failed to earn a spot in the matchday squad.
City welcomed back central defender Lewin Nyatanga and midfielder Kalifa Cisse back to their starting line-up following respective ankle and groin injuries, with Chris Wood dropping to the bench.
Chances were few and far between in the early exchanges, with Smith lashing over the crossbar from long range and James producing a top-class save to turn Chopra's effort to safety, as Ipswich slowly dominated.
City struggled to create openings of any note, and it took until the 22nd minute for the Robins to test McCarthy, with Fontaine seeing his shot from inside the penalty area pushed around the post by the on-loan stopper.
However, Ipswich quickly went down the other end and claimed the lead.
Jay Emmanuel-Thomas sent Martin clear down the right and the midfielder produced a pinpoint cross to pick out Chopra, who made no mistake in heading past James.
It was the former Cardiff man's 13th strike of the campaign and it heaped further pressure on the Tractor Boys' beleaguered guests.
Emmanuel-Thomas fired a thunderbolt from 40 yards marginally over the bar and then showed a more delicate side to chip James, only to see his attempt drift narrowly wide.
And only two good stops from the former England international to deny Chopra prevented Ipswich from taking a bigger lead into the interval.
City pulled themselves back into the game after half-time, reducing the home side to a limited number of chances, although James had to be alert to hold onto Drury's effort from the edge of the area.
But with 25 minutes remaining, Ipswich put the game beyond the visitors.
Drury swung in a corner from the right and Smith rose highest to head beyond James.
Given that City had failed to score in any of their previous five away matches in all competitions prior to the trip to Suffolk, any sort of comeback seemed improbable.
And so it proved as, after Smith's header crashed against the bar, Drury rounded off a successful afternoon with a stunning finish from 25 yards.
Substitutes Wood and Yannick Bolasie both called McCarthy into action in the dying stages, but Ipswich eased to victory.