On a day when promotion rivals QPR, Swansea and Norwich all won it was crucial the Bluebirds kept up with the pace in the battle to win promotion to the Premier League.
Points matter more than performances at this stage in the season and Chopra looked to have produced the only moment of inspiration to head home Craig Bellamy's cross after 65 minutes.
That was until on-loan Arsenal forward Emmanuel-Thomas made the points safe with a stunning effort out of nothing in injury time.
They were only the ninth and 10th league goals conceded by Hull at the KC Stadium this term and ended the home side's nine-match unbeaten run, while Cardiff have now lost just one of their last 10.
Bellamy returned from illness to skipper Cardiff while Stephen McPhail came into the centre of midfield to replace on-loan Seyi Olofinjana, who - despite having permission - was denied the chance to line up against his parent club due to a knee injury.
Hull made just the one change, Jay Simpson coming in for Tijani Belaid, and included on-loan Cardiff centre-back Anthony Gerrard in their ranks who, like season-long loanee Olofinjana, was allowed to come up against his employers.
Jay Bothroyd had the ball in the back of the net after 15 minutes only to see the flag raised for offside.
The Bluebirds striker was again at the centre of matters shortly after as he went down in the penalty area, only to see his appeals waved away by referee Paul Tierney.
The first real moment of threat came after 28 minutes as Matty Fryatt forced Tom Heaton to tip his effort around a post, with Bothroyd called upon to clear Gerrard's goalbound header off the line from the resulting corner.
Chopra then saw Cardiff's second reasonable penalty appeal dismissed having been brought down.
And in the last action of the opening 45 minutes, Bluebirds centre-back Dekel Keinan saw his header blocked on the line by the efforts of Corry Evans.
Gerrard was forced off due to injury at half-time, but replacement centre-half Jack Hobbs was eased into the action as both sides struggled to pose an attacking threat after the restart.
The first real chance of the second half came in the 65th minute and it was one which effectively settled the encounter, with Hull's defence going missing for the first time in the game.
Bellamy sent in a cross from out wide and Chopra was afforded plenty of space to head past Brad Guzan at the near post.
The Tigers responded by bringing on Nick Barmby and he sent a great chance over the bar from six yards just four minutes later.
Hull pressed late on in a bid for a late equaliser but continued to lack that killer instinct in the final third, and Cardiff substitute Emmanuel-Thomas showed them how it was done when he weaved his way through to finish well in injury time and wrap up the win.