Despite a spirited first half showing, Down had too much for the visitors on Saturday evening.
Despite ravelling to Pairc Esler without Tom Prior and Barry McNulty Leitrim started strongly with a two pointer from Killian Gaffney after two minutes.
Ryan O Rourke got Leitrim’s next score after 12 minutes, before Down landed a brace of two pointers from Patrick Havern and Ronan Burns put Down seven ahead after 19 minutes.
Points from Paul Honeyman, Fergal McLoughlin and two efforts from Killian Gaffney, a two pointer and single left Leitrim four behind at the break.
Down led at half-time, 0-12 to 0-8.
Daniel Guinness kicked a two pointer for Down, opening the scoring in the second town. The midfielder scored another two points along with an effort from Michael Rooney leaving Down nine points ahead after 44 minutes.
Leitrim’s opening score of the half finally came on 47 minutes when Paul Honeyman raised a white flag. Ben Guckian and Honeyman added further scores for Leitrim before Down sealed the victory in the closing stages.
A Ruairi McCormack two pointer on 60 minutes set the scene for the final ten minutes when Down hit 1-6.
Ruairi McCormack found the back of the Leitrim net on 67 minutes, as Down set up a meeting with Offaly in the next round as the Tailteann Cup, as Leitrim will face Carlow.
Down running out 14 point winners, 1-27 to 0-16.