The sides traded penalties – and blows – inside the last 10 minutes, with both desperate to find the correct field position from which to tee up a drop goal.
Hull’s Josh Bowden gave them the opportunity, knocking on in his own half, and Gigot did the rest as Hull were defeated for the seventh time in eight visits to Perpignan.
Hull had a 14-8 interval lead after tries from Scott Taylor and Hakim Miloudi – both converted by Jake Connor, who also added a penalty. Catalans replied with a Brayden Williame try, plus conversion and penalty from Josh Drinkwater.
But Catalans were level after the restart, Drinkwater dummied left and stepped right to fool the Hull defence and to touch down. Drinkwater added the goal.
The home side scored back-to-back tries when, from the kick-off, Gigot raced over to score. Drinkwater added the conversion to put the Dragons 20-14 up.
Taylor scored a solo effort, racing clear from 40 metres out, dummying his way past Gigot to score. Connor added the conversion to tie at 20-20.
Connor edged Hull back in front with another penalty goal, but Drinkwater was on hand to level the scores once again with a 40-metre penalty after Josh Griffin had infringed in the ruck.
Both sides were reduced to 12 men in the 64th minute when Connor and Michael McIlorum were sin-binned for fighting before Abdull left the field on a stretcher with an ankle injury.
Catalans took the lead when Miloudi was penalised for a ball-steal on Sam Moa, Drinkwater adding the two points to give the hosts a 24-22 lead.
Connor levelled the game with a 78th-minute penalty before a knock-on by Bowden in the last minute gifted Catalans and Gigot field position to kick a drop-goal with 10 seconds remaining.
Catalans Dragons: Gigot, Broughton, Mead, Wiliame, Tierney, Langi, Drinkwater, Casty, McIlorum, Simon, Jullien, Garcia, Bird.Substitutes: Moa, Anderson, Baitieri, Maria.
Hull: Miloudi, Faraimo, Connor, Griffin, Talanoa, Kelly, Abdull, Taylor, Houghton, Bowden, Manu, Minichiello, Hadley. Substitutes: Tuimavave, Paea, Lane, Matongo.
Referee: James Child (RFL).