With just one point from their last two matches, Cardiff were on top for long spells but the Black Cats never gave up, mounting a grandstand finish without reward.
Chris Brown cancelled out Chopra's early strike, but the former Newcastle United striker had the last word with the winner just before the break.
Sunderland failed to heed an early warning of Chopra's prowess when a mistake by Neill Collins in the second minute gave the lively striker the opportunity to fire high and wide from close range.
But Chopra needed no second chance in the fifth minute, finding himself in front of an open goal after Stan Varga completely misjudged a right-wing centre from Paul Parry to notch his ninth goal of the campaign.
Sunderland, however, were back on level terms five minutes later when Tobias Hysen took on James Chambers and delivered the perfect cross for Brown to head home his third goal of the season.
Chopra returned the compliment for Parry in the 11th minute only for the winger to head over from six yards.
Brown had a shot blocked after good work by Daryl Murphy and Kevin McNaughton saved a certain goal when he took a cross from Murphy off the head of Liam Lawrence.
Cardiff's swift counter attacks though carried much more penetration and it was no surprise when they regained the lead in the 37th minute with a carbon copy goal.
The Sunderland defence was all at sea again from Parry's cross and Chopra moved into double figures with another clinical finish.
Chopra was close to his hat-trick in the 40th minute when his shot looped off Varga into the grateful arms of Darren Ward, while at the other end Hysen missed the chance to send the teams in at the interval on level terms by firing much too high when set up by Dean Whitehead.
Kevin Campbell replaced the injured Steven Thompson at the start of the second half, but there was no let up by the league leaders with only an offside decision denying Chopra his hat-trick in the 48th minute after playing a neat one-two with Riccardo Scimeca.
Sunderland looked hopefully for a penalty when Dwight Yorke was felled by goalkeeper Neil Alexander, but their appeals fell on deaf ears.
Stephen McPhail fired weakly at Ward but Sunderland were denied a 66th minute equaliser when Alexander made a brilliant one-handed save from Hysen's fiercely struck shot.
Chopra and Chambers were booked in stoppage time but the yellow cards failed to take the shine off an accomplished performance.