The City Reds took the lead after just three minutes when Luke Robinson's inside pass put Sean Rutgerson in.
But the Broncos hit back and four tries - against one Salford touchdown - gave them a 10-point lead at half-time.
Salford had most of the ball after the break but touched down just once before Jon Wells rounded off London's victory with the try of the match.
Salford coach Karl Harrison
"Some of our guys weren't at the races. "We lost the game in the first half not the second half when we got sloppy defensively and left ourselves too much to do.
"I think we played okay for long spells and when we got back to 18-12 I thought we could win but it wasn't to be."
London: McLinden, Wells, Smith, Sykes, O'Halloran, Dorn, Leuluai, Tookey, Tookey, Highton, Armour, Armour, Hopkins, Purdham, Mbu, Haumono, Lolohea.
Replacements: Haumono for O'Halloran (16), Trindall for Tookey (19), Haumono for Tookey (69), Lolohea for Armour (13), Tookey for Armour (46), Williams for Mbu (32), Mbu for Haumono (55), Armour for Lolohea (34).
Salford: Hodgson, Hartley, Littler, McAvoy, Stewart, McGuinness, Robinson, Stringer, Alker, Rutgerson, Sibbit, Shipway, Charles, Highton, Highton, Haggerty.
Replacements: Coley for McGuinness (29), Haggerty for Stringer (15), Highton for Rutgerson (42), Highton for Sibbit (6), Clough for Highton (23), Rutgerson for Highton (61), Stringer for Haggerty (69).
Att: 2,997
Ref: Karl Kirkpatrick (Warrington).
MMIX
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