Carayol, who netted in Boro's 2-2 draw with Bolton on New Year's Day, curled home with six minutes remaining before sealing the 2-0 victory in added time.
An entertaining opening period saw Blackpool, who have now lost eight of their last nine games in all competitions, create the first two opportunities of note inside the first 10 minutes.
Middlesbrough had without chances of their own. With the home side operating a high backline, Emanuel Ledesma created two glorious openings with lofted balls over the top of the back four.
The first, on 13 minutes, sent Lukas Jutkiewicz through on goal, but as he prepared to pull the trigger Cathcart came to the home side's rescue with a brilliant last-ditch tackle.
Just minutes later and a near-identical move saw Ledesma send Albert Adomah clear, but this time it was the turn of Jack Robinson to produce a last-gasp block.
Though susceptible at the back, Blackpool remained a threat going forward and after Ricardo Fuller headed straight at Given from Ferguson's long throw-in on 30 minutes, Angel Martinez stung the palms of the veteran goalkeeper with a 25-yard volley.
After the break Ince's men again looked to seize the early initiative, with Chris Basham heading wide of goal from a Neal Bishop right-wing cross, before a succession of corner kicks put the visitors under a concerted period of pressure.
The game was then halted for close to 10 minutes after Blackpool youngster Tom Barkhuizen suffered a nasty head injury and Nathan Eccleston replaced him on the hour mark as he trudged off the pitch.
Moments later Basham should have done better when he headed wide an in-swinging free-kick from Ferguson down the left, before Ince drew a save out of Given with an 18-yard shot.
Boro appeared subdued but they were nearly roused from their slumber by a moment of individual brilliance.
With 69 minutes on the clock, Jutkiewicz was hacked to the floor by Gary Mackenzie down the right side of the penalty area and from the resulting free-kick Ledesma's ferocious, bending shot cannoned off the crossbar.
That effort proved to be a sign of things to come as minutes later a counter-attack saw Carayol cut in from the right before bending a fine effort into the bottom right-hand corner.
And Boro wrapped up the three points deep into injury-time when the Blackpool defence failed to deal with Adomah's cut-back down the left, allowing Carayol to fire into the top left-hand corner to heap more misery on Ince and Blackpool.