In the second half, Ever Banega should have put Unai Emery's men ahead when he surged through the middle of the Gijon defence, but he smashed his strike straight at Cuellar.
Yevhen Konoplyanka carved out an opening for himself by raiding into the box and beating his man, but his low effort drifted inches past the post from a tight angle.
Cuellar made another fine stop to keep the scores level as he dived low to his right to prevent Banega's powerful strike from nestling in the bottom corner.
The home side finally opened the scoring from the penalty spot in the 75th minute after Luis Hernandez brought down Llorente in the box, which resulted in a red card for the defender.
Gamiero took the spot kick and buried his effort past Cuellar to hand his side the lead.
The Frenchman doubled his tally to secure the match for Emery's men when he latched on to Konoplyanka's pinpoint cross into the box to head his effort into the net.
Banega came within inches of netting a third goal for the hosts as he collected the ball on the edge of the box, but his strike was denied by the woodwork with Cuellar beaten.
The win lifts Sevilla into seventh place, while Gijon remain in 14th.