Galway disposed of the Leitrim challenge with a powerful display at a sun-drenched Pairc Sean Mhic Diarmada, Carrick-on-Shannon on Saturday.
The Tribesmen got off to a dream start with two goals, firstly by Jerry Kelleher in the fourth minute, followed two minutes later by an effort from man of the match Shane Maughan.
The visitors scored a further three points before Leitrim finally got off the mark with a Felim McHugh point from play in the 14th minute.
Despite the huge early deficit, Leitrim took the game to their stronger and better organised opponents. They were led by midfielder McHugh and aided by the free-taking of centre half-forward Donal Wrynn.
Lack of firepower up front was the home side's weakness throughout though.
And they were not helped by a robust Galway defence.
Although the Tribesmen deservedly led 2-6 to 0-6 at the interval, the game remained open going into the second half.
Two early second-half Leitrim points sandwiched between a Maughan pointed free for Galway gave the large home support some hope but this was quickly dashed with a second-half Galway goal blitz.
Kelleher added to his first half effort in the 45th minute followed four minutes later with Galway's fourth goal by substitute Ian Burke to put the game beyond a gallant, but limited, Leitrim, who kept trying to the end.
SCORERS -- Galway: J Kelleher 2-1, S Maughan 1-7 (5f), I Burke 1-1, S Walsh 0-2, P Glynn, G Armstrong 0-1 each. Leitrim: D Wrynn 0-6 (6f), F McHugh 0-3, C Farrell, N Moore 0-1 each.
GALWAY -- C Gleeson; L Silke, J Shaughnessy, C Cunningham; E Walsh, S Geoghegan, C Mulryan; E Walsh, G Canavan; S Walsh, C Rabbitte, P Glynn; G Armstrong, S Maughan, J Kelleher. Subs: A Nolan for E Walsh, S Moran for C Cunningham, I Burke for G Armstrong, C Timmon for C Mulryan, S Hughes for J Kelleher.
LEITRIM -- B Flynn; E Madden, D Keane, R Broughton; T Mulvey, K McGloin, S Quinn; F McHugh, C Farrell; N Woods, D Wrynn, N Plunkett; N Moore, M Ferguson, A McLoughlin. Subs: J Connolly for N Woods, G Plunkett for N Plunkett, C Clinton for A McLoughlin, J Fanning for D Keane, B Beirne for N Moore.
REF -- P Neilan (Roscommon).