The victory, their first at Bloomfield Road since September 2000, moves Oscar Garcia's Seagulls three points clear of Blackpool as they close in on a top-six berth.
For the Seasiders, however, it is now six games without a win and means they have won just one of their last six home matches.
Brighton's Leonardo Ulloa fired over from just inside the penalty area after receiving Will Buckley's low free-kick on eight minutes but chances were limited early on.
Ulloa had Brighton's next good chance too, but failed to trouble Matt Gilks from a free-kick when Buckley was tripped by Gary MacKenzie just outside the area on 20 minutes.
Brighton continued to look the more threatening though, and three minutes later Ulloa clattered the post with a curling effort which had Gilks well beaten.
The hosts received another let-off on the half-hour, when Brighton captain Liam Bridcutt released Buckley on the right-wing, but Ashley Barnes could not connect with his low cross.
At the other end Dan Gosling's side-footed volley went well over on 34 minutes, but Blackpool rarely threatened Tomasz Kuszczak's goal in the first half.
And Brighton's dominance paid off when Calderon was allowed to cut inside and, with space opening up before him, beat Gilks with a low, left-footed effort despite the keeper getting a hand to it.
Blackpool showed a renewed vigour early in the second half, with Gosling seeing a low shot blocked just seconds after the restart.
The ex-Everton youngster was involved again on 50 minutes when Kuszczak fumbled a high cross under pressure from the midfielder, but the ball bounced to safety.
Tom Ince then saw a well-struck effort flash wide after he raced on to a loose ball in the penalty area on 70 minutes.
Blackpool were unable to maintain their pressure however and the fans made their frustrations clear, not least when boss Paul Ince replaced striker Michael Chopra with Steven Davies on 74 minutes.
Buckley could have put the result beyond all doubt on 79 minutes as he raced on to a long ball, but Gilks beat away his attempted lob.
At the other end Barry Ferguson's 20-yard free-kick was deflected wide by the wall two minutes later, and the resultant corner came to nothing.
Chris Basham's powerful header, from another Ferguson free-kick, was then well saved by Kuszczak on 83 minutes, but Blackpool were unable to force an equaliser.
Blackpool boss Paul Ince highlighted the importance of the January transfer window in his programme notes, and this latest defeat may see next month take on an added significance for the Seasiders.