It was a second win of the campaign for Pete McGrath's Erne men who had lost three in a row and they move off the foot of the table.
Fermanagh's top scorer Tomas Corrigan limped off early on but Sean Quigley bagged eight points for the hosts with five frees, two 45s and one from play.
Derry are now bottom following their 5-15 to 2-15 defeat away to Galway.
Goals from Benny Heron and Emmett McGuckin helped Derry to a 2-10 to 2-7 lead at the break in Tuam Stadium, with Danny Cummins and Tom Flynn netting for the hosts.
Galway, with the wind in their favour, surged clear in the second half with Johnny Heaney netting before a Eamonn Brannigan penalty and Shane Walsh goal.
Fermanagh's last two matches are Meath away next week and a home match against Derry.
McGrath's men were 0-8 to 0-7 up at half-time and extended that lead with Aidan Breen scoring three points from play.
However, Keelan Sexton palmed in a 46th-minute goal for Clare against the run of play which proved a wake-up call for the hosts.
Fermanagh rattled off five points in a row to seal the valuable victory.
Fermanagh dug deep for a 0-18 to 1-10 win over Clare to boost their chances of survival in Division Two.