Chelsea also made the last 16 after an added-time header from Olivier Giroud gave them a 2-1 win at Rennes.
Ivan Rakitic gave Sevilla a fourth-minute lead with a thumping first-time shot from outside the penalty area before half-time substitute Wanderson equalised in the 56th and El Haddadi netted a last-gasp winner for the visitors.
Croatia midfielder Rakitic stunned the home side with a precise strike into the bottom right corner and the visitors missed several chances in the first half to double their advantage, with El Haddadi and Diego Carlos coming close.
The Brazilian capped a flowing move when he side-stepped a defender in the area and beat goalkeeper Tomas Vadik with a crisp shot which Jules Kounde failed to clear off the line.
With the match seemingly heading for a draw, the lively El Haddadi struck a sublime shot with his weaker right foot to beat home goalkeeper Evgeni Gorodov and send the Spanish side into the business end of Europe's premier club competition.