In a match lacking goalmouth action, the hosts scored in either half to condemn their guests to a second straight defeat.
Both sides had struggled against lower-league opposition in the third round of the FA Cup last weekend, with Brighton being held to a home draw by Blue Square Premier side Wrexham and City going down 1-0 to npower League Two's Crawley.
But if supporters of either team had been hoping for an impressive response from their players they were let down, as the match lacked verve and excitement.
Brighton took the lead after a turgid opening half-hour when Calderon beat David James with a curling effort from 25 yards.
And Will Buckley settled the game with 18 minutes left, collecting Lewis Dunk's pass to round James and slot home.
City had the first effort on goal after seven minutes, with midfielder Marvin Elliott firing wide from the edge of the area, but opportunities were sparse in the opening quarter-hour.
Calderon had a pot-shot blocked by Lewin Nyatanga at the other end after 18 minutes, as neither side could find the necessary rhythm to break the other down.
Brighton's players wanted a penalty when Craig Mackail-Smith tangled with Nyatanga in the area and went to ground midway through the first half, but referee Keith Stroud remained unmoved.
And that proved to be the last action the former Peterborough forward saw as Mackail-Smith was forced off through injury after the incident, with Will Hoskins coming off the bench in his place.
Moments later the Seagulls' injury troubles worsened as Jake Forster-Caskey was withdrawn, with Alan Navarro replacing the 17-year-old midfielder, and the substitute was immediately involved in the action - hitting a 16-yard effort harmlessly over the crossbar.
The match was in dire need of a moment of quality to spark it into life and it got just that after 37 minutes thanks to Calderon.
The Spaniard picked up the ball 30 yards from goal and unleashed a strike that beat James to the visiting keeper's right.
It was the first effort on target from either side and was enough to give the hosts the half-time lead, although the Seagulls could have been two-up but for a fingertip save from James to turn Ashley Barnes' effort out for a corner.
Brighton started brightly after the interval, with Buckley shooting over the bar from 20 yards after 48 minutes and Navarro followed suit with a similar attempt five minutes later.
With a quarter of the game remaining the match finally started to open up, with Calderon and Barnes firing wide before the hosts made sure of victory after 73 minutes.
Dunk split the City defence in two with a pin-point pass, Buckley ran onto the through-ball and, with James helpless, the midfielder had the simple task of skipping past the former England stopper and slipping the ball into the back of the net.
The visitors had to wait until the final minute for their first and only effort on target, and even then Brett Pitman could not beat Peter Brezovan in the Brighton goal.