Wins to Saints and Wigan this weekend in the play-offs in England.
Saints outmuscled the Broncos four tries to one with Sean Long (2) and Willie Talau scoring in the first half for a 20-6 lead.
Darren Smith added another late four pointer in the second half, while Andrew King was London's only try-scorer in the first period.
Great Britian scrum-half Long's 100th try for Saints keeps the Super League champions on course for a fourth Grand Final appearance in five years.
They now meet old rivals Wigan in next Friday's semi-final at the JJB Stadium after the Warriors beat Warrington 25-12.
St Helens: 24 (20) Tries: Long (2), Talau, Smith Goals: Long (4) defeated London Broncos: 6 (6) Tries: King Goals: Thorman
The Warriors trailed 12-6 at the break following a superb first half from Play-Off debutants Warrington, who scored tries through Darrren Burns and Nathan Wood.
But Wigan stormed back in the second period, with Danny Tickle, Brett Dallas and Craig Smith grabbing the tries as they extended their unbeaten run under Mike Gregory to nine games.
Wigan 25 Tries: Lam, Tickle, Dallas, Smith Goals: Farrell, Tickle 2, Robinson DG: Robinson defeated Warrington 12 Tries: Burns, Wood Goals: Appo 2Like