The hosts had led 14-10 but Hull hit back with 18 unanswered points to move ahead, with Griffin and Albert Kelly among the tryscorers.
Jordan Abdull and Rhys Williams hit back for the Broncos and they had a chance to win it with a penalty under the Hull posts.
But the experienced visitors held firm for their fourth win of the season, moving them up to fifth in the table - level on points with fourth-placed Salford.
The hosts, on their return to Super League this term, have enjoyed success at home, with only Castleford lowering their colours. However, they were left regretting a failure to take their chances in an opening 40 minutes they had the better of.
Tries from Elliot Kear and Eloi Pelissier were all they had to show for their efforts, and the fact Hull remained in touch at 14-10 - through Griffin's brace - was always going to be telling against a side that ruthlessly capitalised on Broncos' mistakes after the drinks break.
Carlos Tuimavave went over just minutes after the re-start, with the Broncos defence caught cold, before Jordan Thompson squeezed over in the corner after Hull stand-off Albert Kelly, who was outstanding with ball in hand, spotted a numerical advantage on his blindside.
Kelly added the fourth after picking up a speculative pass deep in his own half and then ghosting home from 60 metres, before Bureto Faraimo strengthened the visitors' position with 15 minutes to play, picking up the pieces from Scott Taylor's rampaging run right into the heart of a back-pedalling black-shirted defence.
However, the capital side have won plenty of admirers for a fervent commitment to the cause, and they kept their faithful on their feet right to the close.
Alex Walker's beautifully balanced running finally got him just reward, opening up some space to send over stand-off, Abdull.
When top scorer Williams tore down the left-hand touchline with five minutes still to play and score under the sticks, it seemed the Broncos would have the final say on proceedings.
But for Matty Fozard's fumble with the line at his mercy, the outcome might have been very different, as the hosts fell just short of under a balmy west London skyline.
