Noel Dunning’s London side put in a brave effort but Leitrim emerged victorious - winning 1-12 to 2-05 - at a wet Ruislip to move into the Connacht SFC semi-finals.
Leitrim booked a 24 June date with Galway as London's 30-year wait for a championship win was prolonged.
The visitors missed two early goal chances, but led 1-09 to 1-02 at the break with Ciaran Duignan, Michael Foley and James Glancy amongst the scorers.
Chris Donnellan and Brennan swapped goals late in the first half, and while Niall Clinton also netted for London on 65 minutes, Leitrim were too far in front to be troubled.
Led by player-coached Martin Kennedy, the former Dublin under-21 defender, London took their time to get to grips with the visitors in what was a tempestuous affair at times.
Leitrim led 0-05 to 0-02 after 20 minutes play with Ciaran Duignan landing three frees, and Michael Foley (free) and Colin Regan also off the mark. Dara Kinneavey succeeded with two frees for London.
Dessie Dolan snr's men should been further ahead by that point but Declan Maxwell found the side-netting when a goal looked on the cards, and Brennan was also denied by a point-blank save from Brian McBrearty.
As the half ticked on in front of a 1,500-strong crowd, Leitrim moved 0-08 to 0-02 ahead with Duignan converting two further frees, Foley bisecting the posts again and James Glancy finding his range.
But as the rain continued to fall down, the Leitrim defence fell asleep in the closing minute of the first half, allowing Conor Beirne to solo forward and find Donnellan who planted the ball to the Leitrim net and make it a three-point game.
Glancy nabbed a point back in injury-time and just before the half-time whistle, some incisive play from Maxwell set up Brennan for a morale-boosting Leitrim goal.
Now seven points to the good, Leitrim relaxed again after the break, with substitute Niall Clinton, Donnellan and Paul Hehir each tapping over a point for London.
Duignan replied with a free before the Exiles had centre-back Beirne sent off in the 54th-minute for a straight red card offence.
Duignan added a brace of points - one from play - to further increase Leitrim's lead, and with full-forward Paul Hehir also being dismissed for his second bookable offence, London's comeback hopes all but vanished.
Clinton's goal was a deserved one for London, who showed plenty of heart and were only three-point losers to Leitrim in the league, and will have annoyed Dolan who knows his side have plenty to work on before they face Galway in four weeks' time.
LONDON: B McBrearty; R Walsh, M Kennedy, S Boyle; P Morgan, C Beirne, E Kavanagh; D Meehan, P O'Donoghue; F Cleary, F Hehir, C Donnellan (1-1); D Kane, P Hehir (0-1), D Kinneavey (0-2).
Subs used: E Brennan for Morgan, S McKenzie-Smith for Cleary, N Clinton (1-1) for Meehan, K Waldron for O'Donoghue.
LEITRIM: N Gill; C Kennedy, M McGuinness, D Reynolds; B Prior, J McKeon, S Foley; G McCloskey, M Duignan; C Regan (0-1), D Maxwell, M Foley (0-1), D Brennan (1-0), J Glancy (0-2), C Duignan (0-8).
Subs used: F McBrien for Glancy, P Howard for M Foley.
REFEREE: Michael Hughes (Tyrone)