The Spaniard's early strike was the only goal of a game that ended with the home team being booed off.
A second home loss in the space of four days has left early promotion favourites Cardiff wallowing in 17th place while Middlesbrough moved up to eighth.
The manner of the loss also failed to relieve the pressure on Ole Gunnar Solskjaer.
The Cardiff manager rang the changes following his side's second-half collapse against Norwich City on Saturday with returns for Mats Daehli, Tom Adeyemi and Cala and a debut for Bruno Ecuele Manga following his £5million transfer from French club Lorient.
Yet that still could not prevent Middlesbrough taking the lead inside two minutes.
Daniel Ayala was booked for a lunging tackle on Adeyemi but from Peter Whittingham's free-kick, Middlesbrough surged forward to score.
Albert Adomah sped down the right before crossing for Kike to finish right-footed from close range for his fourth goal of the season.
The score was on the counter-attack but Middlesbrough threatened every time they entered Cardiff's half, winning four corners inside the first 30 minutes alone.
Cardiff centre-back Cala was booked as the hosts' defending became more desperate while Anthony Pilkington's wild shot from 30 metres out was as good as it got in attack before half-time.
Damia became the second Middlesbrough player shown a yellow card though defensive partner George Friend almost tip-toed through.
That sparked a counter-attack from Cardiff through Kenwyne Jones and Federico Macheda though Kenneth Omerou, on loan from Chelsea, recovered well to snuff out the danger.
Cardiff's inability to either break down the visitors or prevent the likes of Albert Adomah surging forward prompted a drastic midfield reshuffle to a diamond formation before the break.
But it still took a last-ditch tackle by Ecuel Manga to deny Jelle Vossen after Matthew Connolly was horribly caught out by a simple long ball.
Aron Gunnarsson replaced Macheda at half-time to provide some urgency in midfield yet it failed to lift a side looking desperately short of confidence and Marshall had to make the first telling save of the second-half, pushing Adam Clayton's shot wide.
Cardiff struggled to hold on to the ball long enough to muster any sustained pressure and Middlesbrough rarely appeared stretched beyond their means.
Jones offered a physical presence up front but was a lone threat though and was ruled off-side from Gunnarsson's pin-point cross. Anthony Pilkington managed to deliver just one cross, that went unconverted.
Yet Middlesbrough repeatedly caught Cardiff on the break and only the quick thinking of Marshall snuffed out another chance for Clayton.
Solskjaer threw on summer signings Javi Guerra and Adam Le Fondre in search of an equaliser but fell well short despite a late flurry in injury-time.