The hosts took the lead inside five minutes in remarkable circumstances when Markel Susaeta's corner managed to miss everyone at the near post and sneak in.
The game settled down in the rest of the first half, with neither side creating a clear-cut opening before Bilbao went two up nine minutes into the second half.
Sevilla's chances of getting back into the game were significantly reduced in the 72nd minute when Diogo Figueiras picked up his second yellow card and was sent off.
Bilbao made the visitors pay instantly through Ander Herrera, who arrived at the penalty spot to meet another Iraola cross and power a header into the corner.
Three points for Bilbao mean that they are now the clear favourites to join the two Madrid clubs and Barcelona in next season's Champions League.