Richard Marshall’s side were 10-4 down half an hour, but responded with an attacking blitz that left London floundering at 26-10 with 35 minutes remaining.
The visitors opened the scoring on 10 minutes, with Rhys Williams scoring after an outstanding pass from centre Ben Hellewell and Jarrod Sammut converting.
Halifax withstood a sustained bombardment, with a string of penalties and the sin-binning of hooker Brandon Moore for dissent leaving them hanging on until centre Steve Tyrer scored against the run of play.
With tempers flaring, Ben Johnston and Apirana Pewhairangi were both sin- binned after a scuffle, leaving the home side to play for four minutes with 11 men until Moore returned.
The Broncos scored again when a blind pass from Will Sharp went loose and some slack cover defence allowed Elliot Kear to score at the other end, but Sammut missed the goal.
Halifax got back into it as captain Scott Murrell created back-to-back scores for Shane Grady and Simon Grix, Tyrer adding a single conversion and a penalty as Fax went 16-10 up.
And right on half-time they added an outstanding fourth try, Murrell kicking high to the corner and young winger Connor McGrath applying a brilliant acrobatic finish.
Tyrer’s missed kick saw the home side go to the break leading 20-10 and when the centre scored and converted his own try five minutes after half time, that was effectively that, with Will Lovell scoring a late consolation.
The Broncos continued to probe, and looked the sharper side inside the last 10 minutes, but they scored just once, through Will Lovell with 11 minutes remaining, while the home side had a second sensational finish from McGrath ruled out for a foot in touch.