Fuller opened the scoring with a close-range finish after six minutes and though the Owls had plenty of chances to get back in the game - with Jeremy Helan and Connor Wickham guilty of bad misses - Gosling's second-half strike sealed the points for promotion-chasing Blackpool.
With manager Paul Ince returning to the dug-out on the back of his five-match stadium ban, the Seasiders made the perfect start to the afternoon as they took the lead early on.
Tom Ince whipped a low corner to the near post and Fuller peeled away from his marker to turn the ball home inside the six-yard box.
But the visitors only had themselves to blame for failing to get back on level terms just eight minutes later.
Wickham broke free down the right-hand side of the area and pulled the ball back for the unmarked Helan, eight yards out, but with the goal gaping he somehow side-footed wide.
Wednesday were then gifted a second glorious opportunity to make it 1-1 in the space of three minutes.
Neal Bishop's back-pass sent Wickham straight in on goal, but the on-loan striker's shot was brilliantly saved by Matt Gilks.
With Blackpool seemingly happy to play on the counter-attack, it was the visitors who continued to display the greater attacking threat.
A free-kick from Lewis Buxton found the head of Miguel Llera inside the area and his header flew narrowly wide of Gilks' left-hand post.
And with just two minutes remaining of the opening period, a right-wing cross from Roger Johnson picked out Jose Semedo but his wayward header again let the Seasiders off the hook.
While the Owls were unfortunate not to have at least drawn level prior to half-time the second period was a far more enterprising affair, with chances at both ends.
Jacques Maghoma fired an early sighter over the crossbar for the visitors after 55 minutes before Ince cut in from the left flank and forced a good save out of Damian Martinez with a 20-yard drive two minutes later.
As the game began to open up, the sides continued to trade blows and Gary MacKenzie's header and another Ince drive both forced good saves out of Martinez, either side of Semedo's tame shot on the end of a right-wing cross from Wickham.
The second goal came after 73 minutes as Blackpool went 2-0 in front.
Left-back Tyler Blackett - on loan from Manchester United - broke down the left and pulled the ball back for Gosling, who side-footed home from 10 yards out to seal the victory.