First half goals from Jonathan Maher, Martin Finn and Kevin Walsh helped London to a commanding 3-8 to 0-6 interval lead after they had earlier held a 12-point advantage, but Meath steadily cut into the deficit as Stephen Clynch, Sean Heavey and Clynch again found the net.
London’s woes intensified when Brian Costello was sent off on receipt of a second yellow card eight minutes from the end of normal time and Durnin left them shattered when he belted home that sensational late winner.
Scorers for Meath: S Clynch 2-2, S Heavey 1-2, P Durnin 1-1, N Kirby 0-3.
Scorers for London: M Finn 1-2, J Maher, K Walsh 1-0 each, J Egan 0-3, M Walsh, C Quinn, E Cooney, P Sloane, H Vaughan 0-1 each.
MEATH: S McGann; C Reilly, E Fitzgerald, W Mahady; J Togher, P Fagan, S Morris; S Clynch, S Donoghue; S Heavey, N Kirby, C O Mealoid; K Keoghan, N Horan, J Kelly.
Subs: D Healy for Horan (19), C Fitzsimons for Fagan (25), R Massey for Keoghan (32), P Durnin for Kelly (ht), M Burke for Donoghue (ht).
LONDON: T Williams; E Walsh, B Costello, G Fennelly; M Walsh, PJ Rowe, L Mackey; C Quinn, E Cooney; P Sloane, J Egan, H Vaughan; J Maher, M Finn, K Walsh.
Subs: D Maher for Egan (52), G Hill for M Walsh (60), T Hogan for Sloane (64).
Referee: Patrick Murphy (Carlow).