Clare came close to shocking them last time out and a Leitrim side with little firepower up front gave them a few anxious moments, although the outcome was never in doubt.
That was largely due to the performance of Benny Coulter who kicked seven points from play but few of his colleagues showed the productivity which took them to the All-Ireland final last year.
Down manager James McCartan, understandably, lauded man of the match Coulter for the way in which he guided them into the next round.
“What has been said about Benny I don’t need to repeat it, but he is a key player for us,” said McCartan.
“He has been carrying a few injuries for the last few months and he is coming back into a bit of form because he has shaken them off.”
He said that while there was a lot of work to be done, he was pleased with the way they responded to the challenge after Leitrim hit the front just after half-time.
“Leitrim put it up to us for long periods. Ten minutes into the second half, it was game on and up to us to respond after Leitrim got their goal.
“It was nice to respond to their goal. We were the ones kicking on after their goal and that was encouraging.”
Waterford’s win in London means Leitrim is now the only county not to win a game in the qualifiers since the system was introduced. Saturday’s outcome was predictable, with Leitrim producing a typically honest display. However, they just don’t have the resources to seriously trouble even a misfiring Down side.
“I thought the effort the lads put in and the football they played was terrific,” said manager Mickey Moran. “Down dominated the breaking ball in the second half and that was key at the end of the day.
“Down upped the ante and countered our sweeper again, but I am very proud of the lads. They gave it everything they had. I think we are on a learning curve.”
Down led by 1-5 to 0-6 at the interval despite playing against the strong wind but a goal from a penalty by Marty Clarke after 15 minutes gave them a solid foundation.
Clarke tucked the ball into the bottom-right corner after Leitrim full-back John McKeon was penalised for a foot block as Conor Laverty tried to complete a good move which included taking a return pass from Clarke.
The goal put Down 1-3 to 0-1 in front and it seemed as if the All-Ireland finalists would pull away from there but Leitrim, with seven in defence, rallied superbly and hit three points without reply.
Down were rocked when Leitrim got in for a goal just 90 seconds after the restart when Brian McDonald set up Adrian Croal and the Glencar/Manorhamilton clubman did superbly to finish to the net.
Coulter led the admirable Down response as the All-Ireland finalists hit eight points without reply.
Liam Doyle, Mark Poland, Marty Clarke and Kevin McKernan found the range but it was Coulter who ignited the crowd with some exquisite scores which tore the heart out of Leitrim.
A point from sub Peter Fitzpatrick put Down 1-13 to 1-6 in front after 54 minutes before Mulligan stopped the rot with a pointed free 14 minutes from the end but there was no hope of a late Leitrim rally.
The Páirc Esler crowd of 8,000 gave Coulter a standing ovation as he was hauled ashore in the closing stages. Down eased into the next round but there’s plenty of room for improvement, not least around the middle of the field.
Scorers for Down: B Coulter 0-7, M Clarke 1-2 (1-0p, 1 45), M Poland (1f), C Laverty 0-2, L Doyle, K McKernan, P Fitzpatrick 0-1 each.
Scorers for Leitrim: A Croal 1-1, E Mulligan 0-3fs, R Lowe, B McDonald, J Glancy, C Kelly 0-1 each.
Subs for Down: C Maginn for McComiskey (40), P Fitzpatrick for Duffin (42), C Mooney for Doyle (58), A Carr for Coulter (62), D Raferty for Garvey (65).
Subs for Leitrim: C Kelly for McDonald (inj. 44), C Sheridan for R Lowe (52), B McWeeney for G Reynolds (58), F Clancy for Clarke (65).
Referee: M Sludden (Tyrone).