Crofts got on the scoresheet for the second game in a row, firing home from 10 yards in the 28th minute.
Their hopes of victory improved further when Clarets goalkeeper Tom Heaton was dismissed for two bookable offences and Ulloa made sure of a Seagulls win in the 72nd minute.
Brighton's big Argentinian striker Ulloa got in a good position early on but scuffed an angled left-foot shot after being put through by Rohan Ince.
Ulloa was the Seagulls only recognised forward available with Ashley Barnes having been forced out with a hip problem and Craig Mackail-Smith and Will Hoskins both recovering from long-term injuries.
Brighton's Polish goalkeeper Tomasz Kuszczak did well to block a goalbound effort from Danny Ings after Dean Marney cut in dangerously down the right.
Burnley came close after 20 minutes when Keith Treacy smartly set up the advancing Scott Arfield and his deflected left-foot shot flew just wide of Kuszczak's left hand post.
Brighton midfielder Crofts then put a firm header over from 10 yards following a teasing free kick from Spaniard David Lopez.
Burnley were relieved to see a rasping low drive from Inigo Calderon go wide after a spell of Brighton pressure, but the Clarets were powerless to prevent the hosts breaking the deadlock on 28 minutes.
A surging run down the left by Ulloa had the Burnley defence backpedalling and when his low cross came in Crofts was there to score easily from 10 yards.
Ulloa needed lengthy treatment after landing painfully on his ankle but was able to continue and later crucially headed away from inside his own penalty area following a dangerous ball from Danny Lafferty.
Treacy shot across the face of the goal for Burnley before, at the other end, Buckley was off target from close range, despite being let down by his first touch.
The Clarets had a huge let off a minute before the break when keeper Heaton dashed out of the area to bring down the on-rushing Buckley, with referee Darren Sheldrake showing Heaton only a yellow card.
The visitors won a free kick right on the edge of the area shortly after the break after Ings was fouled, but David Jones put the ball over after attempting a flicked effort.
Buckley tried his luck from 20 yards for the Seagulls but Heaton was well positioned to make the save.
Burnley were reduced to 10 men on 57 minutes when Heaton received a second yellow card for handling the ball twice in the process of releasing it under pressure from Ulloa.
The Seagulls then doubled their advantage and sealed their win with a classic centre forward's goal by Ulloa 17 minutes from time.
The Argentinian rose superbly to head home a pin-point right-wing cross from Buckley.
Burnley striker Sam Vokes was unable to get on the end of a cross from skipper Jason Shackell as Brighton bossed the closing stages and were good value for their victory.