Orlandi opened the scoring when he turned in a David Lopez cross just before half-time before Ulloa sealed the win in stoppage time to boost Albion's play-off aspirations and inflict Cardiff's second home defeat of the season.
But Mackay, who turned 41 on Tuesday, will have been left wondering how his side failed to make the most of a host of chances as they were denied four times by the woodwork and by a superb performance from Brighton keeper Tomasz Kuszczak.
This was Cardiff's first loss in 10 games and their lead at the top of the npower Championship has been cut to five points after Hull's win over Blackburn, although the Welsh club have a game in hand on their Yorkshire rivals.
Cardiff should have put themselves into a handy lead before Orlandi struck with the crucial goal, and their profligacy ultimately proved costly.
In-form Fraizer Campbell, with three goals in three appearances since joining from Sunderland, almost gave the hosts an early lead as his lofted shot from Craig Bellamy's pass just flicked the top of the bar.
Kuszczak saved a low shot from Craig Noone, with Campbell lurking after Bruno Saltor had gifted the ball to Andrew Taylor on the Cardiff left.
Former Manchester United stopper Kuszczak then made a stunning stop to keep out a curling Peter Whittingham effort which was destined for the top corner, although he was fortunate seconds later as he misjudged a Bellamy shot which bounced under his body and up on to the bar.
After David Marshall kept out an Ulloa effort the overworked Kuszczak was soon back in action as Dean Hammond's awful backpass on the edge of his own box played in Bellamy, but the Pole was out quickly to push the ball away from the Wales international, before saving his follow up.
And Brighton punished the Bluebirds by taking the lead against the run of play two minutes before the break. Lopez got away down the right-hand side and his perfect ball into the box found an unmarked Orlandi, who swept the ball beyond Marshall.
The goal knocked Cardiff out of their stride as they struggled to find any rhythm early in the second half, but the introduction of Craig Conway for Noone sparked them to life as the winger whistled in a shot tipped over by Kuszczak, before clipping the bar with a misdirected cross.
Cardiff frustrations increased after Adam El-Abd, who had already been booked, appeared to bring down Bellamy in the box, only for referee Keith Stroud to award a free-kick on the edge of the area.
Cardiff piled on the pressure. Campbell fired over from Matthew Connolly's astute pass and an Aron Gunnarsson header came back off the post, but Ulloa had the last word as his shot from Lopez's pull-back went in off Mark Hudson for his first league goal for the Seagulls.