The Exiles recovered from a shambolic start against Mayo, where they conceded two goals in the opening two minutes, to lead by 2-10 to 2-3 at the break.
Phelan would have feared the worst after a poor start, but an unanswered 2-5 put them in the driving seat and they never looked back.
Scorers for London: M Finn 1-9 (5f), J Maher 1-2, J Egan 0-2, S Ryan, H Vaughan 0-1 each.
Scorers for Mayo: B Hunt 2-0, K Feeney 0-5 (5f), D McDonnell, K Higgins (1f) 0-2 each, D O’Brien 0-1.
LONDON: T Williams; E Walsh, B Costello, G Fennelly; M Walsh, PJ Rowe, L Mackey; C Quinn, D Maher; S Ryan, J Egan, H Vaughan; J Maher, M Finn, K Walsh.
Subs: T Hogan for Mackey (32), P Sloane for Ryan (41), S Egan for J Egan (55), R Darcy for Vaughan (63), E Gleeson for J Maher (66).
MAYO: D O’Brien; S Morley, A Connolly, A Brennan; P O’Flynn, P Connell, S Connell; C Freeman, D McConn; D McDonnell, K Higgins, P O’Grady; D McTighe, K Feeney, B Hunt.
Subs: S Markham for O’Grady (32), G Henry for McTighe (63).
Referee: D Hughes (Carlow).