The visitors impressed in the opening half and led 1-10 to 0-6 at the interval, with their goal coming from an Adrian Marren penalty.
The accurate Mark Breheny accounted for five of the points in that spell with Stephen Coen also in fine shooting form.
Fielding six of the U21 team who lost narrowly to Louth in midweek, Offaly threatened a comeback in the second half, with Bernard Allen finding the back of the net after 41 minutes.
However despite that score, the hosts failed to generate any significant momentum and Sligo hung on for a deserved win. Offaly go into the last round of games needing to beat Tipperary while also hoping that Cavan lose at home to Antrim if they are to avoid a return to the basement division.
Scorers for Offaly: A Sullivan 0-2; K Casey 0-2; B Allen 1-2 (0-2f); N Dunne 0-2; D Kelly 0-1; J Coughlan 0-2 (0-1f); N McNamee 0-1.
Scorers for Sligo: M Breheny 0-5 (0-2f); A Marren 1-4 (1-0p 0-1f); S Coen 0-4; C McGee 0-1 ‘45.
OFFALY:A Mulhall; B Darby, E Rigney, S Pender; J Keane, J Moloney, D Kelly; B Connor, N Smith; G Guilfoyle, A McNamee, A Sullivan; B Allen, N Dunne, K Casey.
Subs: N McNamee for D Kelly (HT), A Keeneghan for A McNamee (52), J Coughlan for N Dunne (61), M Brasil for G Guilfoyle (61).
SLIGO: P Greene; N Ewing, J Martin, R Donovan; C Harrison, M Quinn, J Davey; T Taylor, S McManus; M Breheny, P Hughes, A Costello; S Coen, C McGee, A Marren.
Subs: P McGovern for J Davey (9), N McGuire for J Martin (11), B Egan for P Hughes (42), D Maye for C McGee (61), E Mullin for Stephen Coen (71).
Referee: Derek O’Mahoney (Tipperary).