The Frenchman fired a second-half winner after Bruno Miguel had levelled to condemn the Portuguese to defeat on their Europa League debut
The Frenchman, introduced as a second-half substitute, fired home in the 77th minute after Bruno Miguel had cancelled out Vitolo's opener in the hosts' first appearance in the tournament.
Sevilla's experience in European competition looked set to pay dividends from the outset as they took the game to their Portuguese hosts in a lively first quarter of an hour.
Carlos Bacca was thwarted by keeper Vagner Silva before Marko Marin fizzed a shot onto the outside of the post.
Bacca then came within inches of breaking the deadlock, only to be foiled by Mano's goal-line clearance, as the Portuguese side held on until half-time.
But their resistance was not to last. The excellent Marin slid the ball through to Vitolo after a mazy dribble, allowing the striker to dink the ball calmly over Bacca.
Estoril responded immediately to stun the visitors, as Bruno Miguel tapped home after Evandro's cut-back, prompting Unai Emery to ring the changes as Gameiro and Ivan Rakitic were introduced from the bench.
And it took the former PSG striker just over 10 minutes to make an impact. Shortly after Rakitic had been denied from a free kick, Gameiro rifled home a right-footed shot from inside the area to restore the Spanish side's advantage - one they did not relinquish in the closing stages.
The win puts Emery's side clear at the top of Group H, after Slovan Liberec came from two goals down to draw w2-2 with Freiburg in the other encounter.