The former Manly Sea Eagles half, who's into his fifth season in England, barged over in the final minute, moments after man-of-the-match Will Pryce had landed a crucial late drop-goal for the hosts, who were given a huge scare by the Bulls on their long-awaited return.
Tries from Joe Batchelor, Harvey Barron and Davy Litten, all converted by Pryce, had given the home side an 18-10 halftime lead.
But Bradford, for whom Waqa Blake and Connor Wynne touched down before the break, came storming back in the second period and after Hull-born wing Wynne's second try, two Rowan Milnes' penalties had edged the visitors 20-18 ahead, only for the Black and Whites' late efforts to settle it.
Since the Bulls' last Super League fixture in 2014, the three-time grand final winners have endured two relegations - including a spell in the third tier - three administrations and a liquidation before they reformed in 2017.
Hull, who narrowly missed out on the play-offs last season, were without key forwards John Asiata and Herman Ese'ese, while summer signing Jake Arthur, Leeds coach Brad Arthur's son, was also missing through injury.Â
The Bulls took an early lead on Saturday night when centre Blake burst through the home defence and on to Zac Fulton's pass, before John Cartwright's side hit back to level it up through Batchelor's converted score.
Bradford regained the lead through Wynne after his clear run down the left, but the home side responded with wing Barron muscling his way over in the corner and Pryce's excellent touchline conversion edged his side 12-10 ahead in the 25th minute.
Homegrown Hull centre Litten danced his way over to extend his side's lead and with Pryce adding the extras.
Blake's superb offload sent Wynne in for his second try and after converting, the Bulls hauled themselves level at 18-18 early in the second period.
After exchanging penalty goals, home fullback Milnes landed a superb field goal from 30 yards with three minutes left.
Hull then finished the job in the last minute, with replacement Cust squeezing over from close range to the relief of the home fans in a bumper crowd of 16,653.
