Last year's All-Ireland finalists Down endured a tight squeak against Clare before hanging on to win by a point.
With Caolan Mooney making his debut, Conor Laverty's goal helped Down into a 1-2 to 0-0 lead in Ennis.
However, Timmy Ryan's goal helped Clare draw level and Down led only 1-6 to 1-5 at half-time.
Down moved 1-11 to 1-6 ahead but Clare took control to level at 1-12 to 1-12 but Paul McComiskey's late point earned the Mournemen a fortunate win.
More to follow.
Down: B McVeigh, A Brannigan, D Gordon, B McArdle, D Rooney, K McKernan, K Duffin, L Doyle, K King, C Mooney, M Clarke, M Poland, P McComiskey, B Coulter, C Laverty.
All-Ireland Football qualifiers first round
Clare 1-12 1-13 Down
Laois v Tipperary (Portlaoise, 1900)
Antrim 0-16 1-7 Westmeath
Louth v Meath (Kingspan Breffni Park, 1900)
London 0-15 0-9 Fermanagh
Cavan v Longford (Kingspan Breffni Park, 1700)
Wicklow v Sligo (Aughrim, 1700)
Offaly v Monaghan (Tullamore, 1900)