The Toffees will play their first leg at Goodison Park on March 12 but will not relish the return trip to conflict-torn Ukraine seven days later.
Defending champions Sevilla were paired with Primera Division rivals Villarreal while another highlight of the draw was an all-Italian clash between Fiorentina and Roma
Country protection does not apply at this stage of the competition but Russian and Ukrainian teams were kept apart due to the ongoing instability in the region.
That saw the two Ukrainian sides separated from the main pots and Europa League ambassador Jerzy Dudek drew Everton against Dynamo, who had been placed in the first tie
Dnipro were then paired with 1992 champions Ajax in the second.
Proceedings then continued as an open, unseeded draw, with Russian side Zenit St Petersburg next out and drawn against Torino
Dinamo Moscow, the fourth side affected by UEFA's stipulation, will face 1989 UEFA Cup champions Napoli.
Bundesliga side Wolfsburg were pitted against three-times champions Inter Milan in another appealing tie, while Belgian league leaders Club Brugge face Turkey's Besiktas.
All ties will be played on March 12 and 19.
Source : PA
Source: PA