A first-half goal by Luis Fabiano gave Sevilla the lead before Italian midfielder Enzo Maresca netted twice in the second half.
Malian Frederic Kanoute completed the rout to help Sevilla win their first ever European trophy.
Sevilla are the third Spanish club to win the UEFA Cup following triumphs for Real Madrid and Valencia.
Brazilian striker Fabiano opened the score in the 26th minute after he received Daniel Alves' inch-perfect cross with a fine downward header into the corner of the net.
Sevilla goalkeeper Andres Palop denied Mark Viduka's opportunity to equalize when he brilliantly blocked the Australian's first-time shot inside the area.
Maresca doubled the lead in the 78th minute from the rebound after Kanoute's initial effort was denied by Boro keeper Mark Schwarzer.
The Italian was on the score sheet again six minutes later, when he fired a bouncing shot from the edge of the area past Schwarzer.
Kanoute added to Middlesbrough's misery one minute from time after Schwarzer cleared the ball into the path of the former Tottenham striker who notched home.