Yevhen Konoplyanka threatened to break the deadlock in spectacular fashion early on when his 25-yard free kick drifted inches wide of the post.
Deportivo improved as the first half progressed and took the lead midway through the first half when Lucas went one better than Konoplyanka by firing his low free kick into the bottom corner.
© Getty Images
The hosts were inches away from conceding a second goal early in the second half when a lack of pressure invited a shot from Jonathan Rodriguez, whose curling effort drifted just inches wide of the post.
Despite lacking creativity for most of the evening, Sevilla fought back well and eventually produced the quality required in the final third to get back on level terms with 14 minutes of normal time remaining.
Fernando Llorente held off challenges from a couple of defenders to meet a cross with a header to find Iborra, who slotted home despite appearing to be in an offside position.
Neither side could find a winner late on as Deportivo settled for staying in fifth, while Sevilla remain 10th in the table.