Abdulrehman al Alawi and Abdullah Thuwaini scored in the second half to lift Suwaiq after Mohammed al Mashari had put Fanja in front in the first half.
Fanja opened the scoring in the 43rd minute when Mashari scored from an assist from Raeed Ibrahim.
The Fanja No 10's shot from inside the goal area saw the ball slip through the hands of a rather clumsy Suwaiq goalie Faiz al Rusheidi.
The second half, however, saw the match turn on its head with Suwaiq dominating the proceedings. Alawi headed in from a well-placed lob from Ahmed al Qarni in the 57th minute to make it 1-1.
Suwaiq continued to attack after equalising, putting pressure on the Fanja defence that kept looking more and more fragile as the second-half action progressed.
Suwaiq then dealt the match-winning blow in the 75th minute when Thuwaini deftly flicked the ball in after getting hold of a pass from Abdullah al Ajmi.
The Super Cup trophy was presented to Suwaiq captain Rusheidi by Sayyid Khalid al Busaidy, the Oman Football Association chairman.