A freak goal on 62 minutes proved the difference as Sligo suffered their second defeat in this year's Allianz Football League.
Sligo finished the game with 14 players as Shamrock Gaels' David Quinn received his marching orders on 37 minutes.
Tony McEntee's charges held a four-point lead at the interval with Niall Murphy (2), Seán Carrabine (3) and Alan Reilly on target.
Cavan forward Michael Argue and Sligo marksman Carrabine both received second half black cards from referee Niall Cullen.
With Sligo a point up with eight minutes to go, Paddy Lynch sent in a long, hopeful ball. The ball hit the upright, hit off goalkeeper Aidan Devaney and in to the back of the net.
From there, the Breffni men pushed on and secured the victory and remain unbeaten in Allianz National Football League Division 4.
Sligo manager Tony McEntee spoke to reporters after the game:
Results:
Division 2
Galway 2-17 Offaly 3-10
Division 3
Westmeath 0-10 Longford 0-14
Fermanagh 3-15 Laois 3-9
Division 4
Sligo 0-10 Cavan 1-13
Wexford 0-15 Tipperary 4-4
