Ruairi Corrigan's goal helped Fermanagh lead 1-2 to to 0-1 and while Benny Heron netted for Derry, the Ernemen still led 1-6 to 1-5 at half-time.
However, Cailean O'Boyle's goal helped Derry hit an unanswered 1-3 as they took control early in the second half.
Mark Lynch's fisted third goal put further daylight between the teams.
The final scoreline was flattering for Derry as Fermanagh had looked the better side in the opening period as the Oak Leafers were guilty of giving the ball away on numerous occasions.
However, Fermanagh paid for missing a couple of gilt-edged goal chances while, in contrast, Derry took their goal opportunities to put the game to bed in the second half.
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As Fermanagh made the better start, scores from Sean Quigley and Ruairi Corrigan gave them an immediate two-point advantage and Fermanagh led by four when Corrigan netted after being set up by Paul McCusker.
Two of Fermanagh's early scores could - and probably should - have been goals with Ruairi Corrigan and Declan McCusker efforts skimming over Thomas Mallon's crossbar.
Derry struggled to curb Eoin Donnelly's midfield excellence early on but as Fermanagh paid for dropping a number of chances short, the Oak Leafers fought gave to take a scarcely deserved lead in the 25th minute as Heron blasted to the net.
Points from Tomas Corrigan and Aidan Breen restored's Fermanagh lead at the break but the game turned dramatically in Derry's favour after the restart as they hit an unanswered 1-3 with O'Boyle fisting their second goal.
With Damian Barton introducing the influential Mark Lynch at half-time, Derry were a different side in the second period as a succession of long balls launched towards O'Boyle caused major problems for the Erne defence.
Fermanagh's last chance came and went as Mallon made a fine save to push away at Conall Jones goal effort to keep Derry 2-9 to 1-7 ahead.
After a couple of James Kielt frees extended Derry's lead, the margin became 10 in the 52nd minutes as Lynch beat Fermanagh keeper Chris Snow to a high ball as he knocked ball and man to the net.
Emmett Bradley's midfield excellence was a feature of Derry's impressive second half, as he also contributed a couple of glorious towering points.
WEEKEND ALLIANZ FOOTBALL LEAGUE RESULTS
Saturday
Division 1
Down 0-07  3-15 Donegal
Dublin 2-14 0-14 Kerry
Sunday
Division 1
Cork 1-18  0-12 Mayo
Roscommon 1-09  2-10 Monaghan
Division 2
Derry 3-13  1-10 Fermanagh
Meath 1-10  0-08 Armagh
Tyrone 0-10  0-08 Cavan
Laois 1-10  3-12 Galway
Division 3
Clare 1-11  0-07 Sligo
Limerick 1-12  2-09 Tipperary
Offaly 0-12  0-10 Longford
Westmeath 0-11 2-09 Kildare
Division 4
Louth 2-09 0-09 London
Carlow 0-10 1-12 Antrim
Wexford 0-14  1-10 Leitrim
Wicklow 0-13  1-08 Waterford
Derry fought back from being four points down early on to earn a 3-13 to 1-10 victory over Fermanagh in the Division 2 Football League opener.